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Journal articles on the topic 'Subgrupo de fitting'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Arroyo-Jordá, M., and M. D. Pérez-Ramos. "Fitting classes and lattice formations I." Journal of the Australian Mathematical Society 76, no. 1 (2004): 93–108. http://dx.doi.org/10.1017/s1446788700008727.

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AbstractA lattice formation is a class of groups whose elements are the direct product of Hall subgroups corresponding to pairwise disjoint sets of primes. In this paper Fitting classes with stronger closure properties involving F-subnormal subgroups, for a lattice formation F of full characteristic, are studied. For a subgroup-closed saturated formation G, a characterisation of the G-projectors of finite soluble groups is also obtained. It is inspired by the characterisation of the Carter subgroups as the N-projectors, N being the class of nilpotent groups.

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2

Trofimuk, Alexander. "Solvable groups with restrictions on Sylow subgroups of the Fitting subgroup." Asian-European Journal of Mathematics 09, no. 02 (2016): 1650037. http://dx.doi.org/10.1142/s1793557116500376.

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In this paper, we study solvable groups in which [Formula: see text] is at most 2. In particular, we investigated groups of odd order and [Formula: see text]-free groups with this property. Exact estimations of the derived length and nilpotent length of such groups are obtained.

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3

Franciosi, Silvana, and Francesco de Giovanni. "On the Hirsch-Plotkin radical of a factorized group." Glasgow Mathematical Journal 34, no. 2 (1992): 193–99. http://dx.doi.org/10.1017/s0017089500008715.

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Let the group G = AB be the product of two subgroups A and B. A normal subgroup K of G is said to be factorized if K = (A ∩ K)(B ∩ K) and A ∩ B ≤ K, and this is well-known to be equivalent to the fact that K = AK ∩ BK (see [1]). Easy examples show that normal subgroups of a product of two groups need not, in general, be factorized. Therefore the determination of certain special factorized subgroups is of relevant interest in the investigation concerning the structure of a factorized group. In this direction E. Pennington [5] proved that the Fitting subgroup of a finite product of two nilpotent

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4

Asaad, M., M. Ramadan, and Ayesha Shaalan. "Influence of ?-quasinormality on maximal subgroups of Sylow subgroups of fitting subgroup of a finite group." Archiv der Mathematik 56, no. 6 (1991): 521–27. http://dx.doi.org/10.1007/bf01246766.

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5

Nesin, Ali. "Generalized Fitting subgroup of a group of finite Morley rank." Journal of Symbolic Logic 56, no. 4 (1991): 1391–99. http://dx.doi.org/10.2307/2275483.

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AbstractWe define a characteristic and definable subgroup F*(G) of any group G of finite Morley rank that behaves very much like the generalized Fitting subgroup of a finite group. We also prove that semisimple subnormal subgroups of G are all definable and that there are finitely many of them.

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6

Heinenken, Hermann. "Fitting classes of certain metanilpotent groups." Glasgow Mathematical Journal 36, no. 2 (1994): 185–95. http://dx.doi.org/10.1017/s001708950003072x.

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There are two families of group classes that are of particular interest for clearing up the structure of finite soluble groups: Saturated formations and Fitting classes. In both cases there is a unique conjugacy class of subgroups which are maximal as members of the respective class combined with the property of being suitably mapped by homomorphisms (in the case of saturated formations) or intersecting suitably with normal subgroups (when considering Fitting classes). While it does not seem too difficult, however, to determine the smallest saturated formation containing a given group, the sam

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7

Robinson, Derek J. S. "On metanilpotent groups satisfying the minimal condition on normal subgroups." Journal of Group Theory 22, no. 5 (2019): 809–36. http://dx.doi.org/10.1515/jgth-2018-0210.

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Abstract A comprehensive account is given of the theory of metanilpotent groups with the minimal condition on normal subgroups. After reviewing classical material, many new results are established relating to the Fitting subgroup, the Hirsch–Plotkin radical, the Frattini subgroup, splitting and conjugacy, the Schur multiplier, Sylow structure and the maximal subgroups. Module theoretic and homological methods are used throughout.

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8

Srinivasan, S. "Maximal subgroups of finite groups." International Journal of Mathematics and Mathematical Sciences 13, no. 2 (1990): 311–14. http://dx.doi.org/10.1155/s016117129000045x.

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In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting subgroup of the group.

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9

KHUKHRO, E. I., P. SHUMYATSKY, and G. TRAUSTASON. "RIGHT ENGEL-TYPE SUBGROUPS AND LENGTH PARAMETERS OF FINITE GROUPS." Journal of the Australian Mathematical Society 109, no. 3 (2019): 340–50. http://dx.doi.org/10.1017/s1446788719000181.

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AbstractLet $g$ be an element of a finite group $G$ and let $R_{n}(g)$ be the subgroup generated by all the right Engel values $[g,_{n}x]$ over $x\in G$. In the case when $G$ is soluble we prove that if, for some $n$, the Fitting height of $R_{n}(g)$ is equal to $k$, then $g$ belongs to the $(k+1)$th Fitting subgroup $F_{k+1}(G)$. For nonsoluble $G$, it is proved that if, for some $n$, the generalized Fitting height of $R_{n}(g)$ is equal to $k$, then $g$ belongs to the generalized Fitting subgroup $F_{f(k,m)}^{\ast }(G)$ with $f(k,m)$ depending only on $k$ and $m$, where $|g|$ is the product

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10

Heliel, A. A., M. M. Al-Shomrani та T. M. Al-Gafri. "On weakly ℨ-permutable subgroups of finite groups". Journal of Algebra and Its Applications 14, № 05 (2015): 1550062. http://dx.doi.org/10.1142/s0219498815500620.

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Let ℨ be a complete set of Sylow subgroups of a finite group G, that is, for each prime p dividing the order of G, ℨ contains exactly one and only one Sylow p-subgroup of G. A subgroup H of G is said to be ℨ-permutable of G if H permutes with every member of ℨ. A subgroup H of G is said to be a weakly ℨ-permutable subgroup of G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K ≤ Hℨ, where Hℨ is the subgroup of H generated by all those subgroups of H which are ℨ-permutable subgroups of G. In this paper, we prove that if p is the smallest prime dividing the order of G and th

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11

Srinivasan, S. "Finitep′-nilpotent groups. I." International Journal of Mathematics and Mathematical Sciences 10, no. 1 (1987): 135–46. http://dx.doi.org/10.1155/s0161171287000176.

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In this paper we consider finitep′-nilpotent groups which is a generalization of finitep-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product ofp′-nilpotent groups will be ap′-nilpotent group.

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12

LI, YANGMING, LIFANG WANG та YANMING WANG. "FINITE GROUPS WITH SOME ℨ-PERMUTABLE SUBGROUPS". Glasgow Mathematical Journal 52, № 1 (2009): 145–50. http://dx.doi.org/10.1017/s0017089509990231.

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AbstractLet ℨ be a complete set of Sylow subgroups of a finite group G; that is to say for each prime p dividing the order of G, ℨ contains one and only one Sylow p-subgroup of G. A subgroup H of G is said to be ℨ-permutable in G if H permutes with every member of ℨ. In this paper we characterise the structure of finite groups G with the assumption that (1) all the subgroups of Gp ∈ ℨ are ℨ-permutable in G, for all prime p ∈ π(G), or (2) all the subgroups of Gp ∩ F*(G) are ℨ-permutable in G, for all Gp ∈ ℨ and p ∈ π(G), where F*(G) is the generalised Fitting subgroup of G.

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13

Carocca, Angel, and Rudolf Maier. "The p-Huppert-subgroup and the set of p-quasi-superfluous elements in a finite group." Proceedings of the Edinburgh Mathematical Society 36, no. 2 (1993): 289–97. http://dx.doi.org/10.1017/s0013091500018393.

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Based on the theory of p-supersoluble and supersoluble groups, a prime-number parametrized family of canonical characteristic subgroups Γp(G) and their intersection Γ(G) is introduced in every finite group G and some of its properties are studied. Special interest is dedicated to an elementwise description of the largest p-nilpotent normal subgroup of Γp(G) and of the Fitting subgroup of Γ(G).

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14

Bochtler, Jonas, and Peter Hauck. "Mutually permutable subgroups and Fitting classes." Archiv der Mathematik 88, no. 5 (2007): 385–88. http://dx.doi.org/10.1007/s00013-006-1119-x.

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15

Ballester-Bolinches, A., and L. M. Ezquerro. "A NOTE ON FINITE GROUPS GENERATED BY THEIR SUBNORMAL SUBGROUPS." Proceedings of the Edinburgh Mathematical Society 44, no. 2 (2001): 417–23. http://dx.doi.org/10.1017/s0013091500000018.

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AbstractFollowing the theory of operators created by Wielandt, we ask for what kind of formations $\mathfrak{F}$ and for what kind of subnormal subgroups $U$ and $V$ of a finite group $G$ we have that the $\mathfrak{F}$-residual of the subgroup generated by two subnormal subgroups of a group is the subgroup generated by the $\mathfrak{F}$-residuals of the subgroups.In this paper we provide an answer whenever $U$ is quasinilpotent and $\mathfrak{F}$ is either a Fitting formation or a saturated formation closed for quasinilpotent subnormal subgroups.AMS 2000 Mathematics subject classification: P

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16

DE FALCO, M., F. DE GIOVANNI, C. MUSELLA, and Y. P. SYSAK. "GROUPS OF INFINITE RANK IN WHICH NORMALITY IS A TRANSITIVE RELATION." Glasgow Mathematical Journal 56, no. 2 (2013): 387–93. http://dx.doi.org/10.1017/s0017089513000323.

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AbstractA group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is a periodic (generalized) soluble group in which all subnormal subgroups of infinite rank are normal, then either G is a T-group or it has finite rank. It follows that if G is an arbitrary group whose Fitting subgroup has infinite rank, then G has the property T if and only if all its subnormal subgroups of infinite rank are normal.

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17

Soules, Panagiotis. "Two-generator subgroups of soluble groups and their Fitting subgroups." Archiv der Mathematik 80, no. 5 (2003): 449–57. http://dx.doi.org/10.1007/s00013-003-0765-5.

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18

Lowe, Patricia A. "Examination of Latent Test Anxiety Profiles in a Sample of U.S. Adolescents." International Education Studies 14, no. 2 (2021): 12. http://dx.doi.org/10.5539/ies.v14n2p12.

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The present study examined latent test anxiety profiles in a sample of 592 U.S. adolescents in grades 6-12 using latent profile analysis (LPA). The adolescents were administered a multidimensional measure of test anxiety in their schools. The results of LPA indicated that a three-profile test anxiety model provided the best fitting model. The three latent test anxiety subgroups were named low, medium, and high test anxiety. In addition, grade-level and gender were added as covariates to the model and LPA was performed again. Grade-level and gender were found to differentially predict membershi

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19

Vorob'ev, N. T. "Locality of solvable subgroup-closed Fitting classes." Mathematical Notes 51, no. 3 (1992): 221–25. http://dx.doi.org/10.1007/bf01206382.

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20

Espuelas, Alberto. "The fitting length of the Hughes subgroup." Journal of Algebra 105, no. 2 (1987): 365–71. http://dx.doi.org/10.1016/0021-8693(87)90201-8.

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21

Wagner, F. O. "The Fitting Subgroup of a Stable Group." Journal of Algebra 174, no. 2 (1995): 599–609. http://dx.doi.org/10.1006/jabr.1995.1142.

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22

Makarfi, Muhammad Umar. "A characterisation of cyclic subnormal separated A-groups of nilpotent length three." Bulletin of the Australian Mathematical Society 56, no. 2 (1997): 243–51. http://dx.doi.org/10.1017/s0004972700030987.

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The paper gives a detailed description of all those finite A-groups of nilpotent length three that satisfy the cyclic subnormal separation condition. It is shown that every monolithic group under discussion is an extension of its Fitting subgroup P, which is a homocyclic p-group, by a p′ metabelian subgroup H, where p is a prime. The centraliser of P in H is trivial while the monolith W is equal to ω1(P) and the action of H on W is faithful and irreducible. H is further shown to have non trivial centre and is an extension of its derived subgroup M by a subgroup L such thatfor all primes q wher

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23

Berger, T. R., R. A. Bryce, and John Cossey. "Quotient closed metanilpotent Fitting classes." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 38, no. 2 (1985): 157–63. http://dx.doi.org/10.1017/s1446788700023004.

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AbstractA Fitting class of finite soluble groups is one closed under the formation of normal subgroups and products of normal subgroups. It is shown that the Fitting classes of metanilpotent groups which are quotient group closed as well are primitive saturated formuations.

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24

Ercan, Güli̇n, and İsmai̇l Ş. Güloğlu. "Frobenius action on Carter subgroups." International Journal of Algebra and Computation 30, no. 05 (2020): 1073–80. http://dx.doi.org/10.1142/s0218196720500319.

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Let [Formula: see text] be a finite solvable group and [Formula: see text] be a subgroup of [Formula: see text]. Suppose that there exists an [Formula: see text]-invariant Carter subgroup [Formula: see text] of [Formula: see text] such that the semidirect product [Formula: see text] is a Frobenius group with kernel [Formula: see text] and complement [Formula: see text]. We prove that the terms of the Fitting series of [Formula: see text] are obtained as the intersection of [Formula: see text] with the corresponding terms of the Fitting series of [Formula: see text], and the Fitting height of [

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25

KAPLAN, GIL, and DAN LEVY. "SCHREIER CONDITIONS ON CHIEF FACTORS AND RESIDUALS OF SOLVABLE-LIKE GROUP FORMATIONS." Bulletin of the Australian Mathematical Society 78, no. 1 (2008): 97–106. http://dx.doi.org/10.1017/s0004972708000506.

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AbstractLet α be a formation of finite groups which is closed under subgroups and group extensions and which contains the formation of solvable groups. Let G be any finite group. We state and prove equivalences between conditions on chief factors of G and structural characterizations of the α-residual and theα-radical of G. We also discuss the connection of our results to the generalized Fitting subgroup of G.

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26

Yangming, Li. "Some notes on the minimal subgroups of Fitting subgroups of finite groups." Journal of Pure and Applied Algebra 171, no. 2-3 (2002): 289–94. http://dx.doi.org/10.1016/s0022-4049(01)00126-8.

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27

Arroyo-Jordá, M., and M. D. Pérez-Ramos. "Fitting classes and lattice formations II." Journal of the Australian Mathematical Society 76, no. 2 (2004): 175–88. http://dx.doi.org/10.1017/s1446788700008880.

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AbstractGiven a lattice formation F of full characteristic, an F - Fitting class is a Fitting class with stronger closure properties involving F -subnormal subgroups. The main aim of this paper is to prove that the associated injectors possess a good behaviour with respect to F -subnormal subgroups.

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28

Zagurskii, V. N., and N. T. Vorob’ev. "Fitting Classes with Given Properties of Hall Subgroups." Mathematical Notes 78, no. 1-2 (2005): 213–18. http://dx.doi.org/10.1007/s11006-005-0117-9.

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29

Guo, Wenbin, and E. P. Vdovin. "Carter subgroups and Fitting heights of finite groups." Archiv der Mathematik 110, no. 5 (2018): 427–32. http://dx.doi.org/10.1007/s00013-017-1143-z.

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30

DE MELO, EMERSON, and PAVEL SHUMYATSKY. "FITTING SUBGROUP AND NILPOTENT RESIDUAL OF FIXED POINTS." Bulletin of the Australian Mathematical Society 100, no. 1 (2018): 61–67. http://dx.doi.org/10.1017/s0004972718001272.

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Let $q$ be a prime and let $A$ be an elementary abelian group of order at least $q^{3}$ acting by automorphisms on a finite $q^{\prime }$-group $G$. We prove that if $|\unicode[STIX]{x1D6FE}_{\infty }(C_{G}(a))|\leq m$ for any $a\in A^{\#}$, then the order of $\unicode[STIX]{x1D6FE}_{\infty }(G)$ is $m$-bounded. If $F(C_{G}(a))$ has index at most $m$ in $C_{G}(a)$ for any $a\in A^{\#}$, then the index of $F_{2}(G)$ is $m$-bounded.

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31

Ercan, G., and I. Ş. Güloĝlu. "On the Fitting length of generalized Hughes subgroup." Archiv der Mathematik 55, no. 1 (1990): 5–9. http://dx.doi.org/10.1007/bf01199108.

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32

BEIDLEMAN, J. C., and H. HEINEKEN. "GROUPS WITH SUBNORMAL NORMALIZERS OF SUBNORMAL SUBGROUPS." Bulletin of the Australian Mathematical Society 86, no. 1 (2012): 11–21. http://dx.doi.org/10.1017/s0004972710032855.

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AbstractWe consider the class of solvable groups in which all subnormal subgroups have subnormal normalizers, a class containing many well-known classes of solvable groups. Groups of this class have Fitting length three at most; some other information connected with the Fitting series is given.

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33

Boboshko, Mariya Yu, Irina P. Berdnikova, and Natalya V. Maltzeva. "The use of speech sentence audiometry in a free sound field." Science and Innovations in Medicine 5, no. 1 (2020): 36–39. http://dx.doi.org/10.35693/2500-1388-2020-5-1-36-39.

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Objectives -to determine the normative data of sentence speech intelligibility in a free sound field and to estimate the applicability of the Russian Matrix Sentence test (RuMatrix) for assessment of the hearing aid fitting benefit. Material and methods. 10 people with normal hearing and 28 users of hearing aids with moderate to severe sensorineural hearing loss were involved in the study. RuMatrix test both in quiet and in noise was performed in a free sound field. All patients filled in the COSI questionnaire. Results. The hearing impaired patients were divided into two subgroups: the 1st wi

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34

Reid, Colin D. "The Generalised Pro-Fitting Subgroup of a Profinite Group." Communications in Algebra 41, no. 1 (2013): 294–308. http://dx.doi.org/10.1080/00927872.2011.629269.

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35

Hu, Bin, Jianhong Huang, and Alexander Skiba. "On the generalized $\sigma$-Fitting subgroup of finite groups." Rendiconti del Seminario Matematico della Università di Padova 141 (November 20, 2018): 19–36. http://dx.doi.org/10.4171/rsmup/13.

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36

Kilsch, Dieter. "Fitting subgroups of profinite completions of soluble minimax groups." Journal of Algebra 101, no. 1 (1986): 120–26. http://dx.doi.org/10.1016/0021-8693(86)90101-8.

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37

Parh, Md Yasin Ali, Munni Begum, Matthew Harber, Bradley S. Fleenor, Mitchell Whaley, and W. Holmes Finch. "Subgroup identification for differential cardio-respiratory fitness effect on cardiovascular disease risk factors: A model-based recursive partitioning approach." Journal of Statistical Research 54, no. 2 (2021): 147–65. http://dx.doi.org/10.47302/jsr.2020540204.

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The goal of this study is twofold: i) identification of features associated with three cardiovascular disease (CVD) risk factors, and (ii) identification of subgroups with differential treatment effects. Multivariate analysis is performed to identify the features associated with the CVD risk factors: hypertension, diabetes, and dyslipidemia. For subgroup identification, we applied model-based recursive partitioning approach. This method fits a local model in each subgroup of the population rather than fitting one global model for the whole population. The method starts with a model for the ove

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38

Ballester-Bolinches, A., and L. M. Ezquerro. "On a theorem of Bryce and Cossey." Bulletin of the Australian Mathematical Society 57, no. 3 (1998): 455–60. http://dx.doi.org/10.1017/s0004972700031877.

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In this paper we characterise the subgroup–closed Fitting formations of finite groups which are saturated. This is an extension of the Bryce and Cossey result proving the saturation of all subgroup-closed Fitting formations of finite soluble groups.

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39

Hauck, Peter, and Reinhold Kienzle. "Modular fitting functors in finite groups." Bulletin of the Australian Mathematical Society 36, no. 3 (1987): 475–83. http://dx.doi.org/10.1017/s0004972700003774.

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We consider Fitting classes for which the injectors in any finite solvable group are modular subgroups. It is shown that only normal Fitting classes have this property. In fact, we prove two more general results demonstrating that modular Fitting functors and submodular Fitting classes are normal.

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40

Bryce, R. A. "Sub-direct product closed Fitting classes." Bulletin of the Australian Mathematical Society 33, no. 1 (1986): 75–80. http://dx.doi.org/10.1017/s0004972700002896.

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It is shown that in the Fitting class of all finite p-by-q groups, where p and q are different primes, there is among the sub-direct product closed sub-Fitting classes a unique maximal one: it consists of the groups whose minimal normal subgroups are central.

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41

Eick, Bettina, and Alexander Hulpke. "Computing Hall subgroups of finite groups." LMS Journal of Computation and Mathematics 15 (August 1, 2012): 205–18. http://dx.doi.org/10.1112/s1461157012001039.

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AbstractWe describe an effective algorithm to compute a set of representatives for the conjugacy classes of Hall subgroups of a finite permutation or matrix group. Our algorithm uses the general approach of the so-called ‘trivial Fitting model’.

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42

Beidleman, James C., Ben Brewster, and Peter Hauck. "Fitting functors in finite solvable groups: II." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (1987): 37–55. http://dx.doi.org/10.1017/s0305004100066391.

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This paper is a continuation of [1], where we introduced the concept and investigated the basic properties of Fitting functors for finite solvable groups. We recall that a map f which assigns to each finite solvable group G a non-empty set f(G) of subgroups of G is called a Fitting functor if the following property is satisfied: whenever α: G → H is a monomorphism with α(G) ⊴ H, thenThe most prominent examples of conjugate Fitting functors are provided by injectors of Fitting classes. However, Fitting functors f in general do not behave as nicely as injectors. For instance, f(G) need not consi

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43

Förster, Peter. "Nilpotent injectors in finite groups." Bulletin of the Australian Mathematical Society 32, no. 2 (1985): 293–97. http://dx.doi.org/10.1017/s0004972700009965.

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Nilpotent injectors exist in all finite groups.For every Fitting class F of finite groups (see [2]), InjF(G) denotes the set of all H ≤ G such that for each N ⊴ ⊴ G , H ∩ N is an F -maximal subgroup of N (that is, belongs to F and i s maximal among the subgroups of N with this property). Let W and N* denote the Fitting class of all nilpotent and quasi-nilpotent groups, respectively. (For the basic properties of quasi-nilpotent groups, and of the N*-radical F*(G) of a finite group G3 the reader is referred to [5].,X. %13; we shall use these properties without further reference.) Blessenohl and

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44

Busetto, Giorgio, and Enrico Jabara. "The Fitting length of finite soluble groups I Hall subgroups." Archiv der Mathematik 106, no. 5 (2016): 409–16. http://dx.doi.org/10.1007/s00013-016-0895-1.

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45

Adkins, Bryan, and David Caldwell. "Firm or subgroup culture: where does fitting in matter most?" Journal of Organizational Behavior 25, no. 8 (2004): 969–78. http://dx.doi.org/10.1002/job.291.

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46

Cossey, John. "Groups of odd order in which every subnormal subgroup has defect at most two." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 51, no. 2 (1991): 331–42. http://dx.doi.org/10.1017/s1446788700034285.

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AbstractIn 1980, McCaughan and Stonehewer showed that a finite soluble group in which every subnormal subgroup has defect at most two has derived length at most nine and Fitting length at most five, and gave an example of derived length five and Fitting length four. In 1984 Casolo showed that derived length five and Fitting length four are best possible bounds.In this paper we show that for groups of odd order the bounds can be improved. A group of odd order with every subnormal subgroup of defect at most two has derived and Fitting length at most three, and these bounds are best possible.

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47

Beidleman, James C., and Howard Smith. "On frattini-like subgroups." Glasgow Mathematical Journal 35, no. 3 (1993): 408. http://dx.doi.org/10.1017/s001708950000999x.

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Theorem 3 of the paper, published in the Glasgow Mathematical Journal 35 (1993), 95–98, is stated incorrectly.The subgroup G′ ∩ L(G) is nilpotent but not, in general, finitely generated (a suitable counterexample being provided by the group whose presentation is given n the Introduction). In groups with the property σ the Fitting radical is itself finitely generated and so the conclusion of Theorem 3 holds in this special case. The words “finitely generated” should be deleted from the paragraph preceding the statement of Theorem 4, but both this theorem and its proof are correct.

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48

Chi, Zhang, and Alexander N. Skiba. "On two sublattices of the subgroup lattice of a finite group." Journal of Group Theory 22, no. 6 (2019): 1035–47. http://dx.doi.org/10.1515/jgth-2019-0039.

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Abstract:

Abstract Let {\mathfrak{F}} be a non-empty class of groups, let G be a finite group and let {\mathcal{L}(G)} be the lattice of all subgroups of G. A chief {H/K} factor of G is {\mathfrak{F}} -central in G if {(H/K)\rtimes(G/C_{G}(H/K))\in\mathfrak{F}} . Let {\mathcal{L}_{c\mathfrak{F}}(G)} be the set of all subgroups A of G such that every chief factor {H/K} of G between {A_{G}} and {A^{G}} is {\mathfrak{F}} -central in G; {\mathcal{L}_{\mathfrak{F}}(G)} denotes the set of all subgroups A of G with {A^{G}/A_{G}\in\mathfrak{F}} . We prove that the set {\mathcal{L}_{c\mathfrak{F}}(G)} and, in th

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de Melo, Emerson. "Nilpotent residual and fitting subgroup of fixed points in finite groups." Journal of Group Theory 22, no. 6 (2019): 1059–68. http://dx.doi.org/10.1515/jgth-2019-0047.

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Abstract:

Abstract Let q be a prime and A a finite q-group of exponent q acting by automorphisms on a finite {q^{\prime}} -group G. Assume that A has order at least {q^{3}} . We show that if {\gamma_{\infty}(C_{G}(a))} has order at most m for any {a\in A^{\#}} , then the order of {\gamma_{\infty}(G)} is bounded solely in terms of m. If the Fitting subgroup of {C_{G}(a)} has index at most m for any {a\in A^{\#}} , then the second Fitting subgroup of G has index bounded solely in terms of m.

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50

Skiba, Alexander N. "On sublattices of the subgroup lattice defined by formation Fitting sets." Journal of Algebra 550 (May 2020): 69–85. http://dx.doi.org/10.1016/j.jalgebra.2019.12.013.

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