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Journal articles on the topic 'Regular subgroup'

Author: Grafiati

Published: 9 March 2023

Last updated: 19 July 2025

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1

Li, Baojun, Yan Wu, and Lü Gong. "On regular subgroup functors of finite groups." Open Mathematics 20, no. 1 (2022): 1838–44. http://dx.doi.org/10.1515/math-2022-0549.

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Abstract A subgroup functor τ \tau is said Φ \Phi -regular if for all primitive groups G G , whenever H ∈ τ ( G ) H\in \tau \left(G) is a p p -subgroup and N N is a minimal normal subgroup of G G , then ∣ G : N G ( H ∩ N ) ∣ = p d | G:{N}_{G}\left(H\cap N)| ={p}^{d} for some integer d d . In this article, we investigate groups in which some primary subgroups are τ \tau -subgroups for a Φ \Phi -regular subgroup functor τ \tau , and we obtain new criteria for the supersolubility or p p -nilpotency of a group.

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2

Wang, Yanpeng, Binzhou Xia, and Sanming Zhou. "Subgroup regular sets in Cayley graphs." Discrete Mathematics 345, no. 11 (2022): 113023. http://dx.doi.org/10.1016/j.disc.2022.113023.

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3

Mourad, Lougine Mostafa El-Khousht Mahmoud, Medhat Ahmed Elzainy, and Safaa Ismail Hussein. "Comparing the Effect of Activated Charcoal Whitening Agents against Regular Whitening Toothpastes on the Enamel Surface of Premolar Teeth: In vitro Study." Open Access Macedonian Journal of Medical Sciences 10, no. D (2022): 493–98. http://dx.doi.org/10.3889/oamjms.2022.11057.

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INTRODUCTION: There has been increase in demand to use natural whitening agents nowadays which include activated charcoal. Activated charcoal has gained popularity recently with various claims to its benefits that have not been proven. AIM: The aim of the study was to evaluate the effect of activated charcoal whitening agents and regular whitening tooth paste on enamel surface of first premolars and to compare between the effects of materials used. MATERIALS AND METHODS: Twenty-one mandibular first premolars were used and divided into control group: untreated teeth that were later incorporated into experimental group. Experimental group: Consisting of three subgroups: Subgroup I: treated with Carbon Coco. Subgroup II: treated with Venu activated charcoal. Subgroup III: treated with Crest 3D white. Brushing was done nine s for 30 days then teeth were preserved in artificial saliva. RESULTS: Scanning electron microscopic results showed areas with rodless enamel more observed in Subgroup III than Subgroups I and II. EREs were more numerous on Subgroups I and II than Subgroup III on enamel surface. Partially occluded EREs with precipitates were more observed on Subgroups I and II than Subgroup III. Energy dispersive X-ray analysis results for calcium showed significant increase between all groups with control. The highest value was recorded in Subgroup II followed by Subgroups I and III while control group was the lowest one. Phosphorous showed significant increase between all groups with control. The highest value was recorded in Subgroup I followed by Subgroups III and II while control group was the lowest one. Micro-hardness results of Subgroups I and II showed significant increase compared to control group and no significant difference between control and Subgroup III was detected. CONCLUSION: Powder form activated charcoal is more abrasive than whitening toothpastes. There is no visible difference between pure 100% activated charcoal powder and charcoal powder with additives to it.v

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4

Baumeister, Barbara. "Primitive permutation groups with a regular subgroup." Journal of Algebra 310, no. 2 (2007): 569–618. http://dx.doi.org/10.1016/j.jalgebra.2006.09.027.

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5

Pillay, Anand. "Some remarks on modular regular types." Journal of Symbolic Logic 56, no. 3 (1991): 1003–11. http://dx.doi.org/10.2307/2275067.

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Here we consider some problems concerning regular types. In the first place we consider a strongly minimal set D. One can ask what is the strength of the assumption that D has (full) elimination of imaginaries (namely, every definable set X over D has as canonical parameter some tuple from D). We show that D cannot be locally modular. Nontriviality of D is immediate. However, to exclude the locally modular nontrivial case one has to understand structures of the form G/E, where G is a modular strongly minimal group and E is a definable equivalence relation on G with finite classes. We show that the quotient structure G/E can be obtained in two steps. First quotient by a finite subgroup K of G to obtain a strongly minimal group H. Now let Γ be a finite subgroup of the group Aff(H) of definable affine automorphisms of H (namely maps of the form x → αx + a, where α is a definable automorphism of H and a ∈ H), and quotient H by Γ (namely form the orbit space of H under Γ). It can clearly be arranged that Γ contains no nontrivial subgroup of translations.In the second place we look at a nontrivial modular regular type p whose pregeometry is actually a geometry. The geometry is then known to be (infinite-dimensional) projective geometry over a division ring F. We ask whether F is definable (internally to p). If F is finite, this is clear. In fact in this case p must have U-rank 1. So we assume F to be infinite. We are only able to show definability of F in the case where F is a field, using some results on 2-transitive subgroups of PGL [V]. Moreover in the superstable case we also observe that p is isolated.

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6

Ahmadi, Hadi, and Bijan Taeri. "Finite groups with regular join graph of subgroups." Journal of Algebra and Its Applications 15, no. 09 (2016): 1650170. http://dx.doi.org/10.1142/s021949881650170x.

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Let [Formula: see text] be a non-trivial finite group different from a cyclic [Formula: see text]-group. The join graph of [Formula: see text] is a graph whose vertex set is the set of all proper subgroups of [Formula: see text] which are not contained in the Frattini subgroup of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are joined by an edge if and only if [Formula: see text]. In this paper we classify finite groups with regular graphs and determine their graphs.

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7

Dobson, Edward, Cai Heng Li, and Pablo Spiga. "Permutation Groups Containing a Regular Abelian Hall Subgroup." Communications in Algebra 40, no. 9 (2012): 3532–39. http://dx.doi.org/10.1080/00927872.2011.590956.

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8

Kamornikov, S. F. "On The Lattice of Regular Transitive Subgroup Functors." Siberian Mathematical Journal 51, no. 5 (2010): 824–29. http://dx.doi.org/10.1007/s11202-010-0083-7.

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9

Wang, Xiaomeng, and Shou-Jun Xu. "On subgroup regular sets in Cayley sum graphs." Discrete Mathematics 347, no. 9 (2024): 114059. http://dx.doi.org/10.1016/j.disc.2024.114059.

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10

Nakano, Tetsuo. "Regular actions of simple algebraic groups on projective threefolds." Nagoya Mathematical Journal 116 (December 1989): 139–48. http://dx.doi.org/10.1017/s0027763000001732.

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The purpose of this note is to study regular actions of simple algebraic groups on projective threefolds as an application of the theory of algebraic threefolds, especially Mori Theory and the theory of Fano threefolds (cf. Mori [11], Iskovskih [7, 8]). The motivation for this study is as follows. In a series of papers, Umemura, in part jointly with Mukai, has classified maximal connected algebraic subgroups of the Cremona group of three variables and also constructed minimal rational threefolds which correspond to such subgroups (cf. Umemura [16-19], Mukai-Ume-mura [12]). In particular, Umemura and Mukai studied in [12] the SL(2, C)-equivariant smooth projectivization of SL(2, C)/G, where G is a binary icosahedral or octahedral subgroup of SL(2, C). The study of equivariant smooth projectivization of SL(2, C)/G for any finite subgroup G has been completed along their lines in Nakano [14]. The main trick of these studies is the investigation of equivariant contraction maps of extremal rays in the context of Mori Theory [11]. In this note, we apply a similar idea to projective threefolds with a regular action of a simple algebraic group and determine which simple algebraic groups can act regularly and nontrivially on projective threefolds and in which fashion. We also need some standard (but difficult) facts from the theory of Fano threefolds. For the precise statement, see Theorem 1 in the main text. For the proof of this theorem, we need a classification of closed subgroups of simple algebraic groups of codimension 1 and 2, which could be derived easily from the classical work of Dynkin [4]. However, we shall give a geometric proof independent of [4] which leads up directly to the proof of Theorem 1. On the whole, we shall establish by geometric methods the scarcity of closed subgroups of small codimension in simple algebraic groups, which is implied in Dynkin [4].

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11

Korhonen, Mikko. "Unipotent elements forcing irreducibility in linear algebraic groups." Journal of Group Theory 21, no. 3 (2018): 365–96. http://dx.doi.org/10.1515/jgth-2018-0003.

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Abstract Let G be a simple algebraic group over an algebraically closed field K of characteristic {p>0} . We consider connected reductive subgroups X of G that contain a given distinguished unipotent element u of G. A result of Testerman and Zalesski [D. Testerman and A. Zalesski, Irreducibility in algebraic groups and regular unipotent elements, Proc. Amer. Math. Soc. 141 2013, 1, 13–28] shows that if u is a regular unipotent element, then X cannot be contained in a proper parabolic subgroup of G. We generalize their result and show that if u has order p, then except for two known examples which occur in the case {(G,p)=(C_{2},2)} , the subgroup X cannot be contained in a proper parabolic subgroup of G. In the case where u has order {>p} , we also present further examples arising from indecomposable tilting modules with quasi-minuscule highest weight.

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12

Gould, Victoria. "Left orders in regular ℋ-Semigroups II". Glasgow Mathematical Journal 32, № 1 (1990): 95–108. http://dx.doi.org/10.1017/s0017089500009101.

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We make the convention that if a is an element of a semigroup Q then by writing a–1 it is implicit that a lies in a subgroup of Q and has inverse a–1 in this subgroup; equivalently, a ℋ a2 and a–1 is the inverse of a in Ha.A subsemigroup S of a semigroup Q is a left order in Q and Q is a semigroup of left quotients of S if every element of Q can be written as a–1b where a, b ∈ S and, in addition, every element of S satisfying a weak cancellation condition which we call square-cancellable lies in a subgroup of Q. The notions of right order and semigroup of right quotients are defined dually; if S is both a left order and a right order in Q then S is an order in Q and Q is a semigroup of quotients of S.

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13

Feng, Yan-Quan, and Jin Ho Kwak. "Cubic symmetric graphs of order twice an odd prime-power." Journal of the Australian Mathematical Society 81, no. 2 (2006): 153–64. http://dx.doi.org/10.1017/s1446788700015792.

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AbstractAn automorphism group of a graph is said to be s-regular if it acts regularly on the set of s-arcs in the graph. A graph is s-regular if its full automorphism group is s-regular. For a connected cubic symmetric graph X of order 2pn for an odd prime p, we show that if p ≠ 5, 7 then every Sylow p-subgroup of the full automorphism group Aut(X) of X is normal, and if p ≠3 then every s-regular subgroup of Aut(X) having a normal Sylow p-subgroup contains an (s − 1)-regular subgroup for each 1 ≦ s ≦ 5. As an application, we show that every connected cubic symmetric graph of order 2pn is a Cayley graph if p > 5 and we classify the s-regular cubic graphs of order 2p2 for each 1≦ s≦ 5 and each prime p. as a continuation of the authors' classification of 1-regular cubic graphs of order 2p2. The same classification of those of order 2p is also done.

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14

Gawron, Piotr W., and Witold Tomaszewski. "On arrangment of regular cyclic subgroup in symmetric group." Publicationes Mathematicae Debrecen 53, no. 1-2 (1998): 49–57. http://dx.doi.org/10.5486/pmd.1998.1871.

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15

Leinen, Felix. "Chief Series and Right Regular Representations of Finite p-Groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 2 (1988): 225–32. http://dx.doi.org/10.1017/s1446788700029803.

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AbstractWe study the embeddings of a finite p-group U into Sylow p-subgroups of Sym (U) induced by the right regular representation p: U→ Sym(U). It turns out that there is a one-to-one correspondence between the chief series in U and the Sylow p-subgroups of Sym (U) containing Up. Here, the Sylow p-subgroup Pσ of Sym (U) correspoding to the chief series σ in U is characterized by the property that the intersections of Up with the terms of any chief series in Pσ form σp. Moreover, we see that p: U→ Pσ are precisely the kinds of embeddings used in a previous paper to construct the non-trivial countable algebraically closed locally finite p-groups as direct limits of finite p-groups.

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16

Bérczi, Gergely. "On the Popov–Pommerening conjecture for linear algebraic groups." Compositio Mathematica 154, no. 1 (2017): 36–79. http://dx.doi.org/10.1112/s0010437x17007473.

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Let $G$ be a reductive group over an algebraically closed subfield $k$ of $\mathbb{C}$ of characteristic zero, $H\subseteq G$ an observable subgroup normalised by a maximal torus of $G$ and $X$ an affine $k$-variety acted on by $G$. Popov and Pommerening conjectured in the late 1970s that the invariant algebra $k[X]^{H}$ is finitely generated. We prove the conjecture for: (1) subgroups of $\operatorname{SL}_{n}(k)$ closed under left (or right) Borel action and for: (2) a class of Borel regular subgroups of classical groups. We give a partial affirmative answer to the conjecture for general regular subgroups of $\operatorname{SL}_{n}(k)$.

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17

Kohl, Timothy. "Characteristic subgroup lattices and Hopf–Galois structures." International Journal of Algebra and Computation 29, no. 02 (2019): 391–405. http://dx.doi.org/10.1142/s0218196719500073.

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The Hopf–Galois structures on normal field extensions [Formula: see text] with [Formula: see text] are in one-to-one correspondence with the set of regular subgroups [Formula: see text] of [Formula: see text], the group of permutations of [Formula: see text] as a set, that are normalized by the left regular representation [Formula: see text]. Each such [Formula: see text] corresponds to a Hopf algebra [Formula: see text] that acts on [Formula: see text]. Such regular subgroups need not be isomorphic to [Formula: see text] but must have the same order. One can divide all such [Formula: see text] into collections [Formula: see text], where [Formula: see text] is the set of those regular [Formula: see text] normalized by [Formula: see text] and isomorphic to a given abstract group [Formula: see text], where [Formula: see text]. There exists an injective correspondence between the characteristic subgroups of a given [Formula: see text] and the set of subgroups of [Formula: see text] stemming from the Galois correspondence between sub-Hopf algebras of [Formula: see text] and intermediate fields [Formula: see text], where [Formula: see text]. We utilize this correspondence to show that for certain pairs [Formula: see text], the collection [Formula: see text] must be empty. This also shows that for these [Formula: see text], there do not exist skew braces with additive group isomorphic to [Formula: see text] and circle group isomorphic to [Formula: see text].

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18

Stothers, W. W. "On formulae of Macbeath and Hussein." Glasgow Mathematical Journal 31, no. 1 (1989): 65–70. http://dx.doi.org/10.1017/s0017089500007552.

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In his thesis [1], Hussein considered regular permutations of order 2 and 3 in Sn whose product is an n-cycle. For such a pair, we must havefor some g ≥ 1. Such a permutation pair corresponds to a free cycloidal subgroup of the classical modular group (see, e.g., [3]). Previously the free subgroups and the cycloidal subgroups of fixed genus had been enumerated ([4], [5]).

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19

DIGERNES, TROND, and V. S. VARADARAJAN. "MODELS FOR THE IRREDUCIBLE REPRESENTATION OF A HEISENBERG GROUP." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 04 (2004): 527–46. http://dx.doi.org/10.1142/s021902570400175x.

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In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on compact maximal isotropic subgroups. It is shown that if the Heisenberg group is 2-regular, but the subgroup is not, the "vacuum sector" of the irreducible representation exhibits a fermionic structure. This will be the case, for instance, in a quantum mechanical model based on the 2-adic numbers with a suitably chosen isotropic subgroup. The formulation in terms of Heisenberg groups allows a uniform treatment of p-adic quantum systems for all primes p, and includes the possibility of treating adelic systems.

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20

Agafonova, E. M., and S. Erdes. "Results of two-year follow-up of patients with coxitis and axial spondyloarthritis. The effect of therapy on the progression of coxitis. Part II." Rheumatology Science and Practice 60, no. 5 (2022): 587–93. http://dx.doi.org/10.47360/1995-4484-2022-587-593.

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Coxitis is one of the most common causes of early disability in patients with axial spondyloarthritis (axSpA), but the therapy for this condition has not been developed.Goal. to assess the effect of different treatment regimens on the manifestations of coxitis in patients with axSpA. Material and methods. We analyzed 77 patients with axSpA (ASAS criteria 2009) (23 women and 54 men) followed for at least 2 years with clinical and/or instrumental signs of coxitis. Their average age was 30.8±7.7 years with an average duration of illness of 74.0±90.3 months. Positive for HLA-B27 were 72 (94%) patients. In all patients, the BASRI hip index was assessed for each HJ. The median values of laboratory indicators of inflammation of ESR and CRP were initially high (20.0 mm/h and 14.5 mg/l, respectively), but after 2 years the indicators decreased, including ESR to 8.0 mm/h, and CRP to 5.0 mg/l (p<0.05), what we described in the first message. According to the study design, all patients in the group were divided into three subgroups. In the first subgroup, non-steroidal anti-inflammatory drugs (NSAIDs) were regularly taken in therapeutic doses. The second subgroup included patients who were regularly taking NSAIDs and synthetic basic anti-inflammatory drugs (DMARDs). In the third subgroup, patients were observed with a recommendation to take NSAIDs and regular administration of genetically engineered biological drugs (bDMARDs). In the absence of the effect of therapy and the presence of indications, patients of the studied subgroups were transferred to therapy, which included regular intake of NSAIDs and / or DMARDs in combination with bDMARDs. Results: Baseline, 29 patients were included in the NSAID subgroup, 21 patients received combined therapy with DMARDs and NSAIDs, and 27 patients were treated with NSAIDs+bDMARDs, and 16 of them received them together with DMARDs. Initially, in subgroup 1, radiographic signs of coxitis were present in 6 patients (21%), in subgroup 2 – in 3 (14%), in subgroup 3 – in 10 (37%) patients. Progression of coxitis was noted in 12 (48%), and the number of patients with ssrK≥3 increased from 4 to 40% (p><0.05). By the end of the 2-year follow-up period, only 8 patients out of the initially included 21 patients in the chronic DMARD subgroup continued to be followed up. In this subgroup, a significant decrease in laboratory parameters, such as ESR>< 0.05), what we described in the first message. According to the study design, all patients in the group were divided into three subgroups. In the first subgroup, non-steroidal anti-inflammatory drugs (NSAIDs) were regularly taken in therapeutic doses. The second subgroup included patients who were regularly taking NSAIDs and synthetic basic anti-inflammatory drugs (DMARDs). In the third subgroup, patients were observed with a recommendation to take NSAIDs and regular administration of genetically engineered biological drugs (bDMARDs). In the absence of the effect of therapy and the presence of indications, patients of the studied subgroups were transferred to therapy, which included regular intake of NSAIDs and / or DMARDs in combination with bDMARDs. Results: Baseline, 29 patients were included in the NSAID subgroup, 21 patients received combined therapy with DMARDs and NSAIDs, and 27 patients were treated with NSAIDs+bDMARDs, and 16 of them received them together with DMARDs. Initially, in subgroup 1, radiographic signs of coxitis were present in 6 patients (21%), in subgroup 2 – in 3 (14%), in subgroup 3 – in 10 (37%) patients. Progression of coxitis was noted in 12 (48%), and the number of patients with ssrK≥3 increased from 4 to 40% (p<0.05). By the end of the 2-year follow-up period, only 8 patients out of the initially included 21 patients in the chronic DMARD subgroup continued to be followed up. In this subgroup, a significant decrease in laboratory parameters, such as ESR>< 0.05). By the end of the 2-year follow-up period, only 8 patients out of the initially included 21 patients in the chronic DMARD subgroup continued to be followed up. In this subgroup, a significant decrease in laboratory parameters, such as ESR and CRP (p<0.05), was obtained, but no other differences were obtained. In the NSAIDs+bDMARDs subgroup, during the two-year follow-up, the number of patients increased significantly from 27 to 44, of which 22 received DMARDs. A comparative analysis revealed a significant decrease in BASDAI, BASFI, ASDAS-CRP, ESR and CRP (p><0.05), in this group there was no significant increase in patients with x-ray coxitis (p>0.05).Conclusion: Therapy with bDMARDs preparations significantly reduces the rate of radiographic progression of coxitis in patients with axial spondyloarthritis in comparison with standard therapy (NSAIDs, sulfasalazine, methotrexate) of this disease.

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21

Baumeister, Barbara. "Primitive Permutation Groups of Unitary type with a regular Subgroup." Bulletin of the Belgian Mathematical Society - Simon Stevin 12, no. 5 (2006): 657–73. http://dx.doi.org/10.36045/bbms/1136902604.

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Li, Cai Heng. "The Finite Primitive Permutation Groups Containing an Abelian Regular Subgroup." Proceedings of the London Mathematical Society 87, no. 03 (2003): 725–47. http://dx.doi.org/10.1112/s0024611503014266.

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23

Baddeley, R. W. "Primitive Permutation Groups with a Regular Non-Abelian Normal Subgroup." Proceedings of the London Mathematical Society s3-67, no. 3 (1993): 547–95. http://dx.doi.org/10.1112/plms/s3-67.3.547.

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24

Yun, Bo-Hyeok, Hyon-Mo Shin, Mi-Jung Yun, Jung-Bo Huh, Chang-Mo Jeong, and Eun-Sook Kang. "Effect of morphology and diameter of implant fixture-abutment connection on mechanical failure of implants." Journal of The Korean Dental Association 53, no. 9 (2015): 644–55. http://dx.doi.org/10.22974/jkda.2015.53.9.006.

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Purpose: This study was conducted to evaluate the effect of the fixture abutment connection type and diameter on the screw joint stability in external butt joint for 2nd surgery and internal cone connected type implant system for 1st and 2nd surgery using ultimate fracture strength. Materials and Methods: USII system, SSII system and GSII system of Osstem Implant were used. Each system used the fixture with two different diameters and cement-retained abutments, and tungsten carbide / carbon coated abutment screws were used. Disc shaped stainless steel metal tube was attached using resin-based temporary cement. The experimental group was divided into seven subgroups, including the platform switching shaped specimen that uses a regular abutment in the fixture with a wide diameter in USII system. A static load was increased to the metal tube at 5mm deviated point from the implant central axis until it reached the compression bending strength at a rate of 1mm/min. Then the deformations and patterns of fracture in threaded connection were compared. Results and Conclusion: 1. In the comparison between the Regular diameter, compression bending strength of SSII system was higher than USII system and GSII system. There was no significant difference between USII system and GSII system. 2. In the comparison between wide diameter, compression bending strength was increased in the order of GSII system, USII system, and SSII system. 3. In comparison between the implant diameter, compression bending strength of the wide diameter was greater than the regular diameter in any system(P<0.05). 4. There was no significant difference between the platform switching (III group) and the regular diameter (I group) in USII system. 5. In USII system, fracture of abutment screw and deformation of both fixture and abutment were observed in I, II and III subgroups. 6. Failure pattern of SSII system, which was the fracture of abutment screw and deformation of the abutment and fixture, was observed in both IV and V subgroups. Fracture of some fixtures was observed in subgroup V. 7. Failure pattern of GSII system, which was the fracture of the abutment screw and deformation of the fixture and the abutment, was observed in both VI and VII subgroups. Apart from other subgroups, subgroup VII demonstrated no bending neither the fracture at the top of the fixture. The compressive deformation of internal slope in the fixture was the only thing observed in subgroup VII.

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NEUMANN, PETER M., CHERYL E. PRAEGER, and SIMON M. SMITH. "SOME INFINITE PERMUTATION GROUPS AND RELATED FINITE LINEAR GROUPS." Journal of the Australian Mathematical Society 102, no. 1 (2016): 136–49. http://dx.doi.org/10.1017/s1446788716000343.

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This article began as a study of the structure of infinite permutation groups $G$ in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy min-n, the minimal condition on normal subgroups. The groups $G$ are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal nontrivial normal subgroups, or they have a regular normal subgroup $M$ which is a divisible abelian $p$-group of finite rank. In the latter case the point stabilisers are finite and act irreducibly on a $p$-adic vector space associated with $M$. This leads to our second variation, which is a study of the finite linear groups that can arise.

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AbouElwan, Yasser A., and Maher A. Alderawe. "On Strongly Regular Relation of Canonical Hypergroup." Al-Mukhtar Journal of Basic Sciences 21, no. 2 (2024): 52–57. http://dx.doi.org/10.54172/99p86m22.

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Burris and Sankappanavar established connection between congruence on group G (ring R) and normul subgroup of G (ideal of ring R). In this paper by the same manner, the connection between strongly regular relation defined on canonical hypergroup and normal subcanonical hypergroup of canonical hypergroup is established.

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27

Demil, Anneliese, Mickaël Dourcy, Mutien-Marie Garigliany, et al. "Phylogenetic Analysis of Bovine Respiratory Syncytial Virus (BRSV) Subgroups in Wallonia Region of Belgium in Relation to Current Vaccination Strategies." Vaccines 13, no. 3 (2025): 298. https://doi.org/10.3390/vaccines13030298.

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Background: Bovine respiratory syncytial virus (BRSV) is a major pathogen of the bovine respiratory disease complex and causes regular severe winter outbreaks of respiratory disease in cattle. It is therefore responsible for important economic losses for the farming industry. In this study, the genetic diversity of the circulating BRSV strains in Belgium, which has not been assessed since the end of the 1990s, was investigated. Methods: We analyzed 51 BRSV-positive samples collected from 2015 to 2023. This study is the first report on the circulation of BRSV subgroup VIII in Belgium. Furthermore, co-circulation of subgroups II and III was recorded in the same period. Four commercially available vaccine strains marketed in Belgium were also included in the analysis and they clustered with subgroup II or III. Results: Our findings indicate that different strains of BRSV are circulating in Belgium, including those from subgroups II and VIII, with the subgroup VIII strains being particularly distant from the commercially available vaccine strains. Conclusions: These results highlight the importance of ensuring that the available vaccines efficiently protect against strains from circulating subgroups and assessing the potential circulation of attenuated vaccine strains.

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Hongan, Motoshi. "Note on strongly regular near-rings." Proceedings of the Edinburgh Mathematical Society 29, no. 3 (1986): 379–81. http://dx.doi.org/10.1017/s001309150001782x.

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Let S be a semigroup. An element a of S is called right (resp. left) regular if a=a2x (resp. a=xa2) for some x∈S. If a is regular and right (resp. left) regular, a is called strongly right (resp. left) regular. As is well known, if a is strongly regular (i.e., right and left regular) then it is regular, more precisely, there exists uniquely an element x such that a= a2x,x= x2a and ax=xa, and a is contained in a subgroup of S (and conversely).

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Li, Cai Heng. "Permutation Groups with a Cyclic Regular Subgroup and Arc Transitive Circulants." Journal of Algebraic Combinatorics 21, no. 2 (2005): 131–36. http://dx.doi.org/10.1007/s10801-005-6903-3.

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Croisile, B., T. Carmoi, P. Adeleine, and M. Trillet. "Spelling in Alzheimer's disease." Behavioural Neurology 8, no. 3-4 (1995): 135–43. https://doi.org/10.1002/j.1875-8584.1995.tb00001.x.

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Forty‐two patients with Alzheimer's disease (AD) and 30 matched elderly control subjects were compared in a cross‐sectional study of spelling. On the basis of the results of regular word, non‐regular word and non‐word spelling, a cluster analysis identified four distinct AD subgroups corresponding to different degrees of spelling degradation. The first subgroup did not differ from controls on spelling performance but was impaired on descriptive writing, suggesting a loss of semantic abilities applied to writing. The other subgroups were characterized, when the overall number of misspellings increased, by a progressive impairment of lexical spelling followed by a less pronounced deficit of phonological spelling. Spelling ability was linked to language difficulties, visuo‐constructional disorders and increased severity of dementia, but was not affected by age, duration of illness or memory abilities.

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31

Sperandio, Adriane, Vitória Paixão, Ewin Almeida, et al. "L-glutamine supplementation improves the inflammatory profile of exercised obese elderly." Brazilian Journal of Global Health 1, no. 2 (2021): 78–86. http://dx.doi.org/10.56242/globalhealth;2021;1;2;78-86.

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OBJECTIVE: To elucidate the effect of oral L-glutamine (Gln) supplementation, associated or not with the regular practice of combined-exercise training (CET), on glycemic and lipid profile and systemic inflammatory status in elderly subjects. METHODS: 84 elderly subjects, non-practitioners (NP, n=31) and practitioners of CET (n=53), were supplemented with Gln [0.3g/kg of weight plus 10g of maltodextrin, groups: NP-Gln (n=14), and CET-Gln (n=26)], or placebo [10g of maltodextrin, groups: NP-PL (n=17), and CET-PL (n=27)]. Anthropometric and physical data were assessed. Blood sampling was collected pre and post-30 days of supplementation. RESULTS: NP subgroups showed higher BMI and serum IL-6 levels than CET subgroups before and post-supplementation. Higher serum levels of IL-10 with lower IL-6 and IL-6/IL-10 ratio were observed post-supplementation in the CET-Gln subgroup than pre-supplementation. When the volunteers were separated according to their BMI, higher IL-6 levels were found in all obese (OB) subgroups than in the adequate weight (AW) subgroups before supplementation. This difference was not maintained between OB CET-Gln and AW CET-Gln subgroups post-supplementation. Higher levels of IL-10 with lower IL-6 and IL-6/IL-10 ratio were found in the OB CET-Gln subgroup post-supplementation than pre-supplementation. No differences were found in the glycemic and lipid profile. CONCLUSION: Oral Gln supplementation when associated with the regular practice of CET can modulate the systemic inflammatory status, especially in obese elderly subjects.

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Maulana, Amalia E., and Hadist Genta Pradana. "Regular medical checkup behaviour: preventing is better than curing." Asia Pacific Journal of Marketing and Logistics 30, no. 2 (2018): 478–94. http://dx.doi.org/10.1108/apjml-11-2016-0229.

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Purpose The purpose of this paper is to investigate the factors that drive or impede the intention of Indonesian consumers to perform regular medical checkup (MCU). Design/methodology/approach This study begins with an ethnographic study to ascertain the determinant factors that motivate or hinder an individual from performing regular MCU. The study involved stakeholders in various health services providers, including patients and medical professionals. The quantitative part of this study focuses on “preventive” segment of consumers. A survey was conducted covering 303 respondents, consisting of two sub-segments of people labelled “healthy lifestyle” and “unhealthy lifestyle”. Findings Consumer behaviour with regards to needs for MCU must be categorised not based on demographics, but their health status – preventive or curative. The “preventive” group was found to have differences in triggers and barriers between the healthy vs unhealthy lifestyle subgroups. For the “healthy lifestyle” subgroup, the determining factors for a regular MCU are the perceived benefit of action, social deviance, and cost perception. For the “unhealthy lifestyle” subgroup, the determining factors for a regular MCU are the social deviance, disease heritage, belief in traditional medicine, no urgency and cost perception. Research limitations/implications The qualitative study part indicated the differences between two segments: preventive vs curative. The quantitative study part is only conducted in the preventive segment and not covering the curative segment. It would be interesting to see the differences between these two segments. Practical implications Implication of study: to create contextual marketing communication in each stakeholders/segments – to reach the marketing objectives. Different segment has different issues to handle and need a different marketing communication programme. Originality/value Previous studies have focused on analysing the differences in groups based on their demographics, which does not illustrate a homogenous need for an MCU. This study contributes by addressing that researchers must differentiate between “preventive” and “curative” groups. Additionally, the study of triggers and barriers has interestingly found that the determinant factors for healthy and unhealthy lifestyle are not the same.

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Wood, Georgina, Sharon Evans, Kiri Pointon-Bell, Júlio César Rocha, and Anita MacDonald. "Special Low Protein Foods in the UK: An Examination of Their Macronutrient Composition in Comparison to Regular Foods." Nutrients 12, no. 6 (2020): 1893. http://dx.doi.org/10.3390/nu12061893.

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Special low protein foods (SLPFs) are essential in a low phenylalanine diet for treating phenylketonuria (PKU). With little known about their nutritional composition, all SLPFs on UK prescription were studied (n = 146) and compared to equivalent protein-containing foods (n = 190). SLPF nutritional analysis was obtained from suppliers/manufacturers. Comparable information about regular protein-containing foods was obtained from online UK supermarkets. Similar foods were grouped together, with mean nutritional values calculated for each subgroup (n = 40) and percentage differences determined between SLPFs and regular food subgroups. All SLPF subgroups contained 43–100% less protein than regular foods. Sixty-three percent (n = 25/40) of SLPF subgroups contained less total fat with palm oil (25%, n = 36/146) and hydrogenated vegetable oil (23%, n = 33/146) key fat sources. Sixty-eight percent (n = 27/40) of SLPF subgroups contained more carbohydrate, with 72% (n = 105/146) containing added sugar. Key SLPF starch sources were maize/corn (72%; n = 105/146). Seventy-seven percent (n = 113/146) of SLPFs versus 18% (n = 34/190) of regular foods contained added fibre, predominantly hydrocolloids. Nine percent of SLPFs contained phenylalanine > 25 mg/100 g and sources of phenylalanine/protein in their ingredient lists. Stricter nutritional composition regulations for SLPFs are required, identifying maximum upper limits for macronutrients and phenylalanine, and fat and carbohydrate sources that are associated with healthy outcomes.

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Suksumran, Teerapong. "Left Regular Representation of Gyrogroups." Mathematics 8, no. 1 (2019): 12. http://dx.doi.org/10.3390/math8010012.

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In this article, we examine a subspace L gyr ( G ) of the complex vector space, L ( G ) = { f : f is a function from G to C } , where G is a nonassociative group-like structure called a gyrogroup. The space L gyr ( G ) arises as a representation space for G associated with the left regular representation, consisting of complex-valued functions invariant under certain permutations of G. In the case when G is finite, we prove that dim ( L gyr ( G ) ) = 1 | γ ( G ) | ∑ ρ ∈ γ ( G ) | Fix ( ρ ) | , where γ ( G ) is the subgroup of Sym ( G ) generated by a class of permutations of G and Fix ( ρ ) = { a ∈ G : ρ ( a ) = a } .

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35

Cornut, Christophe, and Jishnu Ray. "Generators of the pro-p Iwahori and Galois representations." International Journal of Number Theory 14, no. 01 (2017): 37–53. http://dx.doi.org/10.1142/s1793042118500045.

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For an odd prime [Formula: see text], we determine a minimal set of topological generators of the pro-[Formula: see text] Iwahori subgroup of a split reductive group [Formula: see text] over [Formula: see text]. In the simple adjoint case and for any sufficiently large regular prime [Formula: see text], we also construct Galois extensions of [Formula: see text] with Galois group between the pro-[Formula: see text] and the standard Iwahori subgroups of [Formula: see text].

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36

Pozdnyakova, A. A., L. A. Marchenko, N. K. Runikhina, N. V. Sharashkina, and T. Yu Ivanets. "Metabolic profile and functional state of vascular endothelium in women with various forms of premature ovarian insufficiency." Gynecology 20, no. 3 (2018): 36–41. http://dx.doi.org/10.26442/2079-5696_2018.3.36-41.

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Objective. Compare levels of biochemical and functional markers of cardiovascular risk in the molecular-genetic and autoimmune forms of premature ovarian insufficiency (POI). Materials and methods. The study included 68 women with POI, 49 of them - with molecular-genetic form (a subgroup IA), 16 women with autoimmune form (a subgroup IB), 3 women - idiopathic form (a subgroup IC), and 85 women with regular periods (group II - control). Hormonal profile, levels of biochemical and functional markers of endothelial dysfunction [total cholesterol (TC), triglycerides, low density lipoproteins (LDL), high density lipoproteins, atherogenic index, apolipoproteins A1 and B, uric acid, high-sensitivity C-reactive protein (hsCRP), glucose, insulin, insulin resistance index HOMA, right and left carotid intima-media thickness (cIMT), brachial artery flow-mediated dilatation (FMD)] were assessed in all the participants. Results. The levels of cholesterol, LDL, cIMT were statistically significantly increased in subgroups IA and IB compared to group II. The patients with autoimmune form of POI (subgroup IB) had statistically increased levels of cholesterol and LDL compared to group with molecular-genetic form (subgroup IA). The women in subgroup IA also had significantly increased levels of uric acid, a highly sensitive CRP, endothelin-1 and decreased brachial artery FMD in comparison with the control group. Conclusion. Molecular-genetic POI is associated with more pronounced adverse changes in the profile of cardiovascular disease risk markers.

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Blyth, T. S., Emília Giraldes, and M. Paula O. Marques-Smith. "Associate subgroups of orthodox semigroups." Glasgow Mathematical Journal 36, no. 2 (1994): 163–71. http://dx.doi.org/10.1017/s0017089500030706.

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A unit regular semigroup [1, 4] is a regular monoid S such that H1 ∩ A(x) ≠ Ø for every xɛS, where H1, is the group of units and A(x) = {y ɛ S; xyx = x} is the set of associates (or pre-inverses) of x. A uniquely unit regular semigroupis a regular monoid 5 such that |H1 ∩ A(x)| = 1. Here we shall consider a more general situation. Specifically, we consider a regular semigroup S and a subsemigroup T with the property that |T ∩ A(x) = 1 for every x ɛ S. We show that T is necessarily a maximal subgroup Hα for some idempotent α. When Sis orthodox, α is necessarily medial (in the sense that x = xαx for every x ɛ 〈E〉) and αSα is uniquely unit orthodox. When S is orthodox and α is a middle unit (in the sense that xαy = xy for all x, y ɛ S), we obtain a structure theorem which generalises the description given in [2] for uniquely unit orthodox semigroups in terms of a semi-direct product of a band with a identity and a group.

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38

Syarifudin, Abdul Gazir, and Verrel Rievaldo Wijaya. "A PYTHON CODE FOR GENERATING ALL PROPER SUBGROUPS OF DIHEDRAL GROUP." Journal of Fundamental Mathematics and Applications (JFMA) 6, no. 1 (2023): 10–17. http://dx.doi.org/10.14710/jfma.v6i1.15939.

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The dihedral group of order 2n denoted by D_2n is the symmetry group of a regular -polygon consisting of rotation and reflection elements and the composition of both elements. Like any other group, the dihedral group also have a subgroup whose numbers differs depending on the value of n. This research is conducted by studying past literature and explore a new development to a theory. In this paper, all the form of proper subgroups of D_2n will be given and all of these proper subgroups of D_2n will be generated and counted with the help of Python program.

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39

Song, Shu Jiao, Cai Heng Li, and Hua Zhang. "Finite permutation groups with a regular dihedral subgroup, and edge-transitive dihedrants." Journal of Algebra 399 (February 2014): 948–59. http://dx.doi.org/10.1016/j.jalgebra.2013.10.022.

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40

Afshar, B., and R. Ameri. "Strongly Regular Relations Derived from Fundamental Relation." Journal of Algebraic Hyperstructures and Logical Algebras 4, no. 2 (2023): 123–30. http://dx.doi.org/10.61838/kman.jahla.4.2.8.

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We introduce a new regular relation δ on a given group G and show that δ is a congurence relation on G, with respect to module the commutator subgroup of G. Then we show that the effect of this relation on the fundamental relation β is equal to the fundamental relation γ, and we conclude that, if ρ is an arbitrary strongly regular relation on the hypergroup H, then the effect of δ on ρ, results in a strongly regular relation on H such that its quotient is an abelian group.

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41

Munn, W. D. "Direct finiteness of certain monoid algebras." Proceedings of the Edinburgh Mathematical Society 39, no. 2 (1996): 365–69. http://dx.doi.org/10.1017/s0013091500023087.

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A semigroup is said to be completely regular if and only if each of its elements lies in a subgroup. It is shown that the algebra of a completely regular monoid (semigroup with identity) over a field of characteristic zero is directly finite.

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42

Loveys, James. "Abelian groups with modular generic." Journal of Symbolic Logic 56, no. 1 (1991): 250–59. http://dx.doi.org/10.2307/2274917.

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AbstractLet G be a stable abelian group with regular modular generic. We show that either1. there is a definable nongeneric K ≤ G such that G/K has definable connected component and so strongly regular generics, or2. distinct elements of the division ring yielding the dependence relation are represented by subgroups of G × G realizing distinct strong types (when regarded as elements of Geq).In the latter case one can choose almost 0-definable subgroups representing the elements of the division ring. We find a bound ((G: G0)) for the size of the division ring in case G has no definable subgroup K so that G/K is infinite with definable connected component. We show in case (2) that the group G/H, where H consists of all nongeneric points of G, inherits a weakly minimal group structure from G naturally, and Th(G/H) is independent of the particular model G as long as G/H is infinite.

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43

Chen, Ruifang, and Xianhe Zhao. "On Conjugacy Class Graph of Normal Subgroup." Algebra Colloquium 29, no. 03 (2022): 437–42. http://dx.doi.org/10.1142/s1005386722000335.

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Let [Formula: see text] be a finite group and [Formula: see text] a normal subgroup of [Formula: see text]. Denote by [Formula: see text] the graph whose vertices are all distinct [Formula: see text]-conjugacy class sizes of non-central elements in [Formula: see text], and two vertices of [Formula: see text] are adjacent if and only if they are not coprime numbers. We prove that if the center [Formula: see text] and [Formula: see text]is [Formula: see text]-regular for [Formula: see text], then either a section of [Formula: see text]is a quasi-Frobenius group or [Formula: see text] is a complete graph with [Formula: see text] vertices.

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44

Pruccoli, Jacopo, Isabelle Mack, Bea Klos, et al. "Mental Health Variables Impact Weight Loss, Especially in Patients with Obesity and Binge Eating: A Mediation Model on the Role of Eating Disorder Pathology." Nutrients 15, no. 18 (2023): 3915. http://dx.doi.org/10.3390/nu15183915.

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Background: Various mental health and eating behavior variables have been independently associated with predicting weight loss in individuals with obesity. This study aims to investigate a mediation model that assesses the distinct contributions of these variables in predicting weight changes in patients with obesity following an outpatient behavioral weight loss intervention (BWLI). Methods: General mental health (depression, anxiety, stress, impulsivity), eating behavior (cognitive restraint, disinhibition, hunger), eating disorder pathology, and body mass index (BMI) were assessed in a group of 297 patients with obesity at the admission of a BWLI program. BMI was re-evaluated during the final treatment session. A mediation model was employed to examine whether mental health and eating behavior variables predicted BMI changes, with eating disorder pathology serving as a mediator. The model was tested both overall and within two patient subgroups: those with regular binge eating (≥four episodes/month) and those without. Results: In the overall sample (n = 238), the relationships between depression, impulsivity, and cognitive restraint with BMI change were mediated by eating disorder pathology. In the subgroup with regular binge eating (n = 99, 41.6%), the associations between stress and disinhibition with BMI change were additionally mediated by eating disorder pathology. In the subgroup without regular binge eating, eating disorder pathology showed no mediating effect. Discussion: Multiple mental health and eating behavior variables assessed at admission predicted BMI changes, particularly when mediated by eating disorder pathology in patients with regular binge eating. A comprehensive psychopathological assessment prior to starting BWLI may help identify multiple factors affecting prognosis and treatment outcomes. Long-term follow-up studies in this field are required.

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45

Brothier, Arnaud, and Vaughan F. R. Jones. "On the Haagerup and Kazhdan properties of R. Thompson’s groups." Journal of Group Theory 22, no. 5 (2019): 795–807. http://dx.doi.org/10.1515/jgth-2018-0114.

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Abstract A machinery developed by the second author produces a rich family of unitary representations of the Thompson groups F, T and V. We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of V that has an almost invariant vector but no nonzero {[F,F]} -invariant vectors reproving and extending Reznikoff’s result that any intermediate subgroup between the commutator subgroup of F and V does not have Kazhdan’s property (T) (though Reznikoff proved it for subgroups of T). Second, we construct a one parameter family interpolating between the trivial and the left regular representations of V. We exhibit a net of coefficients for those representations which vanish at infinity on T and converge to 1 thus reproving that T has the Haagerup property after Farley who further proved that V has this property.

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46

Newman, M. F., and Ming-Yao Xu. "A note on regular metabelian groups of prime-power order." Bulletin of the Australian Mathematical Society 46, no. 2 (1992): 343–46. http://dx.doi.org/10.1017/s0004972700011953.

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Let p be a prime and d, e positive integers. We prove that a regular d-generator metabelian p-group whose commutator subgroup has exponent pe has nilpotency class at most e(p – 2) + 1 unless e = 1, d > 2, p > 2 when the class can be p and these bounds are best possible.

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47

Helm, Jessica, Gulcan Akgul, and Lonnie P. Wollmuth. "Subgroups of parvalbumin-expressing interneurons in layers 2/3 of the visual cortex." Journal of Neurophysiology 109, no. 6 (2013): 1600–1613. http://dx.doi.org/10.1152/jn.00782.2012.

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The input, processing, and output characteristics of inhibitory interneurons help shape information flow through layers 2/3 of the visual cortex. Parvalbumin (PV)-positive interneurons modulate and synchronize the gain and dynamic responsiveness of pyramidal neurons. To define the diversity of PV interneurons in layers 2/3 of the developing visual cortex, we characterized their passive and active membrane properties. Using Ward's and k-means multidimensional clustering, we identified four PV interneuron subgroups. The most notable difference between the subgroups was their firing patterns in response to moderate stimuli just above rheobase. Two subgroups showed regular and continuous firing at all stimulus intensities above rheobase. The difference between these two continuously firing subgroups was that one fired at much higher frequencies and transitioned into this high-frequency firing rate at or near rheobase. The two other subgroups showed irregular, stuttering firing patterns just above rheobase. Both of these subgroups typically transitioned to regular and continuous firing at intense stimulations, but one of these subgroups, the strongly stuttering subgroup, showed irregular firing across a wider range of stimulus intensities and firing frequencies. The four subgroups also differed in excitatory synaptic input, providing independent support for the classification of subgroups. The subgroups of PV interneurons identified here would respond differently to inputs of varying intensity and frequency, generating diverse patterns of PV inhibition in the developing neural circuit.

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Pappas, G., and I. Zachos. "Regular integral models for Shimura varieties of orthogonal type." Compositio Mathematica 158, no. 4 (2022): 831–67. http://dx.doi.org/10.1112/s0010437x22007370.

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We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular $p$ -adic integral models for these varieties over odd primes $p$ at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.

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JAMALI, A. R., and M. VISEH. "ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS." Bulletin of the Australian Mathematical Society 87, no. 2 (2012): 278–87. http://dx.doi.org/10.1017/s0004972712000706.

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AbstractIn this paper we prove that every nonabelian finite 2-group with a cyclic commutator subgroup has a noninner automorphism of order two fixing either Φ(G) or Z(G) elementwise. This, together with a result of Peter Schmid on regular p-groups, extends our result to the class of nonabelian finite p-groups with a cyclic commutator subgroup.

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50

Zelenyuk, Yevhen. "Regular Homeomorphisms of Finite Order on Countable Spaces." Canadian Journal of Mathematics 61, no. 3 (2009): 708–20. http://dx.doi.org/10.4153/cjm-2009-038-x.

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Abstract.We present a structure theorem for a broad class of homeomorphisms of finite order on countable zero dimensional spaces. As applications we show the following.(a) Every countable nondiscrete topological group not containing an open Boolean subgroup can be partitioned into infinitely many dense subsets.(b) If G is a countably infinite Abelian group with finitely many elements of order 2 and βG is the Stone–Čech compactification of G as a discrete semigroup, then for every idempotent p ∈ βG\﹛0﹜, the subset ﹛p,−p﹜ ⊂ βG generates algebraically the free product of one-element semigroups ﹛p﹜ and ﹛−p﹜.

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