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Journal articles on the topic 'Group extension'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Forrest, A. H. "Decomposing isometric extensions using group extensions." Ergodic Theory and Dynamical Systems 13, no. 4 (December 1993): 661–73. http://dx.doi.org/10.1017/s0143385700007604.

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AbstractThis paper studies the structure of isometric extensions of compact metric topological dynamical systems with ℤ action and gives two decompositions of the general case to a more structured case. Suppose that Y → X is a M-isometric extension. An extension, Z, of Y is constructed which is also a G-isometric extension of X, where G is the group of isometries of M. The first construction shows that, provided that (X, T) is transitive, there are almost-automorphic extensions Y′ → Y and X′ → X, so that Y′ is homeomorphic to X′ × M and the natural projection Y′ → X′ is a group extension. The second shows that, provided that (X, T) is minimal, there is a G-action on Z which commutes with T and which preserves fibres and acts on each of them minimally. Each individual orbit closure, Za, in Z is a G′-isometric extension of X, where G′ is a subgroup of G, and there is a G′-action on Za which commutes with T, preserves fibres and acts minimally on each of them. Two illustrations are presented. Of the first: to reprove a result of Furstenberg; that every distal point is IP*-recurrent. Of the second: to describe the minimal subsets in isometric extensions of minimal topological dynamical systems.

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2

Lafuente, Julio P. "Parametrizing group extension loops." Communications in Algebra 28, no. 6 (January 2000): 2783–800. http://dx.doi.org/10.1080/00927870008826992.

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3

SATO, JUNRO, SUSUMU ODA, and KEN-ICHI YOSHIDA. "ON INTEGRAL DOMAINS WITH CYCLIC GROUP ACTIONS." Journal of Algebra and Its Applications 10, no. 03 (June 2011): 491–508. http://dx.doi.org/10.1142/s0219498811004719.

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Let A be a commutative integral domain with quotient field L, and let R be a subdomain of A with quotient field K. Assuming that L is a Galois extension of K, Nagata required the condition for R to be normal when A is called a Galois extension of R (see p. 31, M. Nagata, Local Rings (Wiley, New York, 1962)). However in this paper, A is considered in the case that R is not necessarily assumed to be normal. We introduce the notion of cyclic Galois extensions of integral domains and investigate several properties of such ring extensions. In particular, we completely determine the seminormalization [Formula: see text] of A in an overdomain B such that both A ⊆B are cyclic Galois extensions of R.

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4

Hoshino, Mitsuo, Noritsugu Kameyama, and Hirotaka Koga. "Group-graded and group-bigraded rings." Journal of Algebra and Its Applications 14, no. 07 (April 24, 2015): 1550100. http://dx.doi.org/10.1142/s0219498815501005.

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Let I be a nontrivial finite multiplicative group with the unit element e and A = ⨁x∈I Ax an I-graded ring. We construct a Frobenius extension Λ of A and study when the ring extension A of Ae can be a Frobenius extension. Also, formulating the ring structure of Λ, we introduce the notion of I-bigraded rings and show that every I-bigraded ring is isomorphic to the I-bigraded ring Λ constructed above.

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5

Rzewuski, Jan. "I. quantization as group extension." Reports on Mathematical Physics 26, no. 3 (December 1988): 335–59. http://dx.doi.org/10.1016/0034-4877(88)90013-4.

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6

Malfait, Wim. "The (outer) automorphism group of a group extension." Bulletin of the Belgian Mathematical Society - Simon Stevin 9, no. 3 (2002): 361–72. http://dx.doi.org/10.36045/bbms/1102715061.

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7

Kumar, Rahul, and Atul Gaur. "Δ-Extension of rings and invariance properties of ring extension under group action." Journal of Algebra and Its Applications 17, no. 12 (December 2018): 1850239. http://dx.doi.org/10.1142/s0219498818502390.

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Let [Formula: see text] be commutative rings with identity such that [Formula: see text]. A ring extension [Formula: see text] is called a [Formula: see text]-extension of rings if [Formula: see text] is a subring of [Formula: see text] for each pair of subrings [Formula: see text] of [Formula: see text] containing [Formula: see text]. In this paper, a characterization of integrally closed [Formula: see text]-extension of rings is given. The equivalence of [Formula: see text]-extension of rings and [Formula: see text]-extension of rings is established for an integrally closed extension of a local ring. Over a finite dimensional, integrally closed extension of local rings, the equivalence of [Formula: see text]-extensions of rings, FIP, and FCP is shown. Let [Formula: see text] be a subring of [Formula: see text] such that [Formula: see text] is invariant under action by [Formula: see text], where [Formula: see text] is a subgroup of the automorphism group of [Formula: see text]. If [Formula: see text] is a [Formula: see text]-extension of rings, then [Formula: see text] is a [Formula: see text]-extension of rings under some conditions. Many such [Formula: see text]-invariant properties are also discussed.

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8

Robinson, E. Arthur. "The Maximal Abelian Sub-Extension Determines Weak Mixing for Group Extensions." Proceedings of the American Mathematical Society 114, no. 2 (February 1992): 443. http://dx.doi.org/10.2307/2159666.

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9

Jamali, A. R. "The Wells exact sequence for the automorphism group of a Lie ring extension." Journal of Algebra and Its Applications 18, no. 03 (March 2019): 1950058. http://dx.doi.org/10.1142/s0219498819500580.

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We give an explicit description of the Wells map for the automorphism group of a Lie ring extension. Using this map, we construct an exact sequence for the automorphism group of a Lie ring extension similar to that for group extensions.

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10

Faul, Peter F. "Baer sums for a natural class of monoid extensions." Semigroup Forum 102, no. 3 (February 19, 2021): 655–73. http://dx.doi.org/10.1007/s00233-020-10156-9.

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AbstractIt is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of extensions to a natural class of extensions of monoids, the cosetal extensions. An extension "Equation missing" is cosetal if for all $$g,g' \in G$$ g , g ′ ∈ G in which $$e(g) = e(g')$$ e ( g ) = e ( g ′ ) , there exists a (not necessarily unique) $$n \in N$$ n ∈ N such that $$g = k(n)g'$$ g = k ( n ) g ′ . These extensions generalise the notion of special Schreier extensions, which are themselves examples of Schreier extensions. Just as in the group case where a semidirect product could be associated to each extension with abelian kernel, we show that to each cosetal extension (with abelian group kernel), we can uniquely associate a weakly Schreier split extension. The characterization of weakly Schreier split extensions is combined with a suitable notion of a factor set to provide a cohomology group granting a full characterization of cosetal extensions, as well as supplying a Baer sum.

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11

Cegarra, A. M., J. M. Garćia-Calcines, and J. A. Ortega. "On Graded Categorical Groups and Equivariant Group Extensions." Canadian Journal of Mathematics 54, no. 5 (October 1, 2002): 970–97. http://dx.doi.org/10.4153/cjm-2002-036-1.

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AbstractIn this article we state and prove precise theorems on the homotopy classification of graded categorical groups and their homomorphisms. The results use equivariant group cohomology, and they are applied to show a treatment of the general equivariant group extension problem.

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12

Vasiu, Adrian. "Extension theorems for reductive group schemes." Algebra & Number Theory 10, no. 1 (February 14, 2016): 89–115. http://dx.doi.org/10.2140/ant.2016.10.89.

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13

Otabe, Shusuke. "An extension of Nori fundamental group." Communications in Algebra 45, no. 8 (October 21, 2016): 3422–48. http://dx.doi.org/10.1080/00927872.2016.1236936.

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14

Antonyan, Sergey, and Manuel Sanchis. "Extension of locally pseudocompact group actions." Annali di Matematica Pura ed Applicata 181, no. 3 (August 2002): 239–46. http://dx.doi.org/10.1007/s102310100039.

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15

BOYLE, MIKE, and SCOTT SCHMIEDING. "Finite group extensions of shifts of finite type: -theory, Parry and Livšic." Ergodic Theory and Dynamical Systems 37, no. 4 (February 11, 2016): 1026–59. http://dx.doi.org/10.1017/etds.2015.87.

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This paper extends and applies algebraic invariants and constructions for mixing finite group extensions of shifts of finite type. For a finite abelian group$G$, Parry showed how to define a$G$-extension$S_{A}$from a square matrix over$\mathbb{Z}_{+}G$, and classified the extensions up to topological conjugacy by the strong shift equivalence class of$A$over$\mathbb{Z}_{+}G$. Parry asked, in this case, if the dynamical zeta function$\det (I-tA)^{-1}$(which captures the ‘periodic data’ of the extension) would classify the extensions by$G$of a fixed mixing shift of finite type up to a finite number of topological conjugacy classes. When the algebraic$\text{K}$-theory group$\text{NK}_{1}(\mathbb{Z}G)$is non-trivial (e.g. for$G=\mathbb{Z}/n$with$n$not square-free) and the mixing shift of finite type is not just a fixed point, we show that the dynamical zeta function for any such extension is consistent with an infinite number of topological conjugacy classes. Independent of$\text{NK}_{1}(\mathbb{Z}G)$, for every non-trivial abelian$G$we show that there exists a shift of finite type with an infinite family of mixing non-conjugate$G$extensions with the same dynamical zeta function. We define computable complete invariants for the periodic data of the extension for$G$(not necessarily abelian), and extend all the above results to the non-abelian case. There is other work on basic invariants. The constructions require the ‘positive$K$-theory’ setting for positive equivalence of matrices over$\mathbb{Z}G[t]$.

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16

Hwang, Yoon-Sung. "A GALOIS EXTENSION WITH GALOIS GROUP DIHEDRAL GROUP OR GENERALIZED QUATERNION GROUP." Communications of the Korean Mathematical Society 20, no. 4 (October 1, 2005): 641–44. http://dx.doi.org/10.4134/ckms.2005.20.4.641.

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17

Zachariasz, Robert. "PERBEDAAN PENGETAHUAN IBU-IBU TENTANG ISU-ISU LINGKUNGAN ANTARA STRATEGI PENYULUHAN OUT GROUP VERSUS IN GROUP BERDASARKAN KEPEDULIAN LINGKUNGAN." Jurnal Ilmiah Pendidikan Lingkungan dan Pembangunan 17, no. 01 (March 31, 2016): 25–33. http://dx.doi.org/10.21009/plpb.171.03.

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The objective of this research is to analyze the effect of extension strategy and the environmental concern on knowledge about environmental issues of house wives on the slums in West Jakarta. The sample of the research was 40 housewives, which selected randomly. The data were analyzed by using ANOVA with 2 x 2 factorial design. The result of the research reveals that: 1) the knowledge about environmental issues of housewiveswho received extension strategy by out group extension agents have not more highly than when they received extension by in group extension agents; 2) The housewives who have high environmental concern and receive extension by out group extension agents have more highly knowledge about environmental issues than when they received extension by in group extension agents; 3)The housewives who have low environmental concern and received extension by out group extension agents have lower knowledge about environmental issues than when they received extension by ingroup extension agents; 4) There are interaction effects between extension strategy and the environmental concern towards the housewives knowledge about environmental issues.

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18

Zachariasz, Robert. "PERBEDAAN PENGETAHUAN IBU-IBU TENTANG ISU-ISU LINGKUNGAN ANTARA STRATEGI PENYULUHAN OUT GROUP VERSUS IN GROUP BERDASARKAN KEPEDULIAN LINGKUNGAN." IJEEM - Indonesian Journal of Environmental Education and Management 1, no. 2 (September 2, 2017): 27–44. http://dx.doi.org/10.21009/ijeem.012.03.

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The objective of this research is to analyze the effect of extension strategy and the environmental concern on knowledge about environmental issues of house wives on the slums in West Jakarta. The sample of the research were 40 housewives which selected randomly. The data were analyzed by using ANOVA with 2 x 2 factorial design. The result of the research reveals that: 1) the knowledge about environmental issues of housewives who received extension strategy by out group extension agents have not more highly than when they received extension by in group extension agents; 2) The housewives who have high environmental concern and receive extension by out group extension agents have more highly knowledge about environmental issues than when they received extension by in group exten-sion agents; 3)The housewives who have low environmental concern and received extension by out group extension agents have lower knowledge about environmen-tal issues than when they received extension by ingroup extension agents; 4) There are interaction effects between extension strategy and the environmental concern towards the housewives knowledge about environmental issues.

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19

GENDRON, T. M., and A. VERJOVSKY. "GEOMETRIC GALOIS THEORY, NONLINEAR NUMBER FIELDS AND A GALOIS GROUP INTERPRETATION OF THE IDELE CLASS GROUP." International Journal of Mathematics 16, no. 06 (July 2005): 567–93. http://dx.doi.org/10.1142/s0129167x05002989.

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This paper concerns the description of holomorphic extensions of algebraic number fields. After expanding the notion of adele class group to number fields of infinite degree over ℚ, a hyperbolized adele class group [Formula: see text] is assigned to every number field K/ℚ. The projectivization of the Hardy space ℙ𝖧•[K] of graded-holomorphic functions on [Formula: see text] possesses two operations ⊕ and ⊗ giving it the structure of a nonlinear field extension of K. We show that the Galois theory of these nonlinear number fields coincides with their discrete counterparts in that 𝖦𝖺𝗅(ℙ𝖧•[K]/K) = 1 and 𝖦𝖺𝗅(ℙ𝖧•[L]/ℙ𝖧•[K]) ≅ 𝖦𝖺𝗅(L/K) if L/K is Galois. If K ab denotes the maximal abelian extension of K and 𝖢K is the idele class group, it is shown that there are embeddings of 𝖢K into 𝖦𝖺𝗅⊕(ℙ𝖧•[K ab ]/K) and 𝖦𝖺𝗅⊗(ℙ𝖧•[K ab ]/K), the "Galois groups" of automorphisms preserving ⊕ (respectively, ⊗) only.

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20

Barrera-Mora, Fernando, and Pablo Lam-Estrada. "Radical extensions and crossed homomorphisms." Bulletin of the Australian Mathematical Society 64, no. 1 (August 2001): 107–19. http://dx.doi.org/10.1017/s0004972700019729.

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If Ω/F is a Galois extension with Galois G and μ(Ω) denotes the group of roots of unity in Ω, we use the group Z1 (G,μ(Ω)) of crossed homomorphisms to study radical extensions inside Ω. Furthermore, we characterise cubic radical extension, and we provide an example to show that this result can not extended for higher degree extensions.

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21

Khanduja, Sudesh K., and Usha Garg. "On extensions of valuations to simple transcendental extensions." Proceedings of the Edinburgh Mathematical Society 32, no. 1 (February 1989): 147–56. http://dx.doi.org/10.1017/s0013091500007008.

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Let ν0 be a valuation of a field K0 with residue field k0 and value group Z, the group of rational integers. Let K0(x) be a simple transcendental extension of K0. In 1936, Maclane [3] gave a method to determine all real valuations V of K0(x) which are extensions of ν0. But his method does not seem to give an explicit construction of these valuations. In the present paper, assuming K0 to be a complete field with respect to ν0, we explicitly determine all extensions of ν0 to K0(x) which have Z as the value group and a simple transcendental extension of k0 as the residue field. If V is any extension of ν0 to K0(x) having Z as the value group and a transcendental extension of k0 as the residue field, then using the Ruled Residue theorem [4, 2, 5], we give a method which explicitly determines V on a subfield of K0(x) properly containing K0.

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22

Ahn, Youngho. "On compact group extension of Bernoulli shifts." Bulletin of the Australian Mathematical Society 61, no. 2 (April 2000): 277–88. http://dx.doi.org/10.1017/s0004972700022280.

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Let ρ : G →  (H) be an irreducible unitary representation of a compact group G where  (H) is a set of unitary operators of finite dimensional Hilbert space H. For the (p1, …, PL)-Bernoulli shift, the solvability of ρ(φ(x)) g (Tx) = g (x) is investigated, where φ(x) is a step function.

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23

Choi, K. H., S. K. Lee, K. S. Kong, and H. Kim. "Extension of SIP for group-based registration." Electronics Letters 48, no. 2 (2012): 91. http://dx.doi.org/10.1049/el.2011.2729.

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24

Ding, J., and S. Khoroshkin. "Weyl group extension of quantized current algebras." Transformation Groups 5, no. 1 (March 2000): 35–59. http://dx.doi.org/10.1007/bf01237177.

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25

Greenberg, Peter, and Vlad Sergiescu. "An acyclic extension of the braid group." Commentarii Mathematici Helvetici 66, no. 1 (December 1991): 109–38. http://dx.doi.org/10.1007/bf02566638.

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26

Biswas, Indranil. "Stable bundles and extension of structure group." Differential Geometry and its Applications 23, no. 1 (July 2005): 67–78. http://dx.doi.org/10.1016/j.difgeo.2005.03.006.

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27

Fisher, Robert J., and H. Turner Laquer. "The extension problem for lie group homomorphisms." Differential Geometry and its Applications 3, no. 2 (June 1993): 169–90. http://dx.doi.org/10.1016/0926-2245(93)90029-z.

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28

Szeto, George, and Lianyong Xue. "On central commutator Galois extensions of rings." International Journal of Mathematics and Mathematical Sciences 24, no. 5 (2000): 289–94. http://dx.doi.org/10.1155/s0161171200004099.

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LetBbe a ring with1,Ga finite automorphism group ofBof ordernfor some integern,BGthe set of elements inBfixed under each element inG, andΔ=VB(BG)the commutator subring ofBGinB. Then the type of central commutator Galois extensions is studied. This type includes the types of Azumaya Galois extensions and GaloisH-separable extensions. Several characterizations of a central commutator Galois extension are given. Moreover, it is shown that whenGis inner,Bis a central commutator Galois extension ofBGif and only ifBis anH-separable projective group ringBGGf. This generalizes the structure theorem for central Galois algebras with an inner Galois group proved by DeMeyer.

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29

Bunk, Severin, Lukas Müller, and Richard J. Szabo. "Smooth 2-Group Extensions and Symmetries of Bundle Gerbes." Communications in Mathematical Physics 384, no. 3 (May 25, 2021): 1829–911. http://dx.doi.org/10.1007/s00220-021-04099-7.

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AbstractWe study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev–Mickelsson–Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-group models within our geometric framework. Starting from a basic gerbe on a compact simply-connected Lie group G, we prove that the smooth 2-group extensions of G arising from our construction provide new models for the string group of G.

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30

Glasner, Eli, and Bernard Host. "Extensions of Cantor minimal systems and dimension groups." crll 2013, no. 682 (May 3, 2012): 207–43. http://dx.doi.org/10.1515/crelle-2012-0037.

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Abstract. Given a factor map of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups in terms of intermediate extensions which are extensions of (Y,S) by a compact abelian group. Then we show that, by contrast, the existence of an intermediate non-abelian finite group extension can produce a situation where the dimension group of (Y,S) embeds into a proper subgroup of the dimension group of (X,T), yet the quotient of the dimension groups is nonetheless torsion free. Next we define higher order cohomology groups associated to an extension, and study them in various cases (proximal extensions, extensions by, not necessarily abelian, finite groups, etc.). Our main result here is that all the cohomology groups are torsion groups. As a consequence we can now identify as the torsion group of the quotient group .

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31

SZCZEPAŃSKI, ANDRZEJ, and ANDREI VESNIN. "HNN EXTENSION OF CYCLICALLY PRESENTED GROUPS." Journal of Knot Theory and Its Ramifications 10, no. 08 (December 2001): 1269–79. http://dx.doi.org/10.1142/s0218216501001438.

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It is shown that if the defining word of a cyclically presented group is admissable then its natural HNN extension is the group of a high dimensional knot. As an example we define a family of cyclically presented groups which contains Sieradski groups, Fibonacci groups, and Gilbert-Howie groups. It is proven that HNN extensions of these groups are LOG groups and so, are fundamental groups of complements of codimension two closed orientable connected tamely embeded ℓ-dimensional manifolds (ℓ≥2).

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32

Szeto, George, and Lianyong Xue. "Skew group rings which are Galois." International Journal of Mathematics and Mathematical Sciences 23, no. 4 (2000): 279–83. http://dx.doi.org/10.1155/s0161171200000624.

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LetS*Gbe a skew group ring of a finite groupGover a ringS. It is shown that ifS*Gis anG′-Galois extension of(S*G)G′, whereG′is the inner automorphism group ofS*Ginduced by the elements inG, thenSis aG-Galois extension ofSG. A necessary and sufficient condition is also given for the commutator subring of(S*G)G′inS*Gto be a Galois extension, where(S*G)G′is the subring of the elements fixed under each element inG′.

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33

Reyes, Edgar N. "Homomorphisms of ergodic group actions and conjugacy of skew product actions." International Journal of Mathematics and Mathematical Sciences 19, no. 4 (1996): 781–88. http://dx.doi.org/10.1155/s0161171296001081.

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LetGbe a locally compact group acting ergodically onX. We discuss relationships between homomorphisms on the measured groupoidX×G, conjugacy of skew product extensions, and similarity of measured groupoids. To do this, we describe the structure of homomorphisms onX×Gwhose restriction to an extension given by a skew product action is the trivial homomorphism.

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34

Chen, Weining, Gaohua Tang, and Huadong Su. "Units on the Gauss extension of a Galois ring." Journal of Algebra and Its Applications 15, no. 02 (October 6, 2015): 1650028. http://dx.doi.org/10.1142/s0219498816500286.

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Ring extensions are a well-studied topic in ring theory. In this paper, we study the structure of the Gauss extension of a Galois ring. We determine the structures of the extension ring and its unit group.

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35

Raposo, A. P. "Skew-symmetric Elements in Nonlinear Involutions in Group Rings." Algebra Colloquium 22, no. 02 (April 15, 2015): 321–32. http://dx.doi.org/10.1142/s1005386715000280.

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Given an involution in a group G, it can be extended in various ways to an involution in the group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear extensions are considered and necessary and sufficient conditions are given on the group G, its involution, the ring R and the extension for the set of skew-symmetric elements to be commutative and for it to be anticommutative.

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36

Szeto, George. "On Azumaya Galois extensions and skew group rings." International Journal of Mathematics and Mathematical Sciences 22, no. 1 (1999): 91–95. http://dx.doi.org/10.1155/s0161171299220911.

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Two characterizations of an Azumaya Galois extension of a ring are given in terms of the Azumaya skew group ring of the Galois group over the extension and a Galois extension of a ring with a special Galois system is determined by the trace of the Galois group.

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37

KOCH, ALAN, and AUDREY MALAGON. "p-ADIC ORDER BOUNDED GROUP VALUATIONS ON ABELIAN GROUPS." Glasgow Mathematical Journal 49, no. 2 (May 2007): 269–79. http://dx.doi.org/10.1017/s0017089507003680.

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AbstractFor a fixed integer e and prime p we construct the p-adic order bounded group valuations for a given abelian group G. These valuations give Hopf orders inside the group ring KG where K is an extension of $\mathbb{Q} _{p}$ with ramification index e. The orders are given explicitly when G is a p-group of order p or p2. An example is given when G is not abelian.

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38

Ichimura, Humio. "Class group of a cyclotomic Zp×Zl-extension." Acta Arithmetica 150, no. 3 (2011): 263–83. http://dx.doi.org/10.4064/aa150-3-4.

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39

Shih, Hsu-Shih, Huan-Jyh Shyur, and E. Stanley Lee. "An extension of TOPSIS for group decision making." Mathematical and Computer Modelling 45, no. 7-8 (April 2007): 801–13. http://dx.doi.org/10.1016/j.mcm.2006.03.023.

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40

Prince, Mel, and Mark Davies. "Moderator teams: an extension to focus group methodology." Qualitative Market Research: An International Journal 4, no. 4 (December 2001): 207–16. http://dx.doi.org/10.1108/eum0000000005902.

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41

Soroka, Dmitrij V., and Vyacheslav A. Soroka. "Gauge semi-simple extension of the Poincaré group." Physics Letters B 707, no. 1 (January 2012): 160–62. http://dx.doi.org/10.1016/j.physletb.2011.07.003.

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42

Hannum, Juliana Santos de Souza, Cristiane Souza Do Carmo, Raissa Ferreira Ávila, Ivoni Félix De Sousa, and Fábio Jesus Miranda. "Psicoeducative Group of Country: project Extension." Fragmentos de Cultura 28, no. 2 (June 18, 2018): 31. http://dx.doi.org/10.18224/frag.v28i2.5452.

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Down syndrome has been much discussed today, but little research has turned to supporting families. Therefore, this study aimed to evaluate an action developed in Alfadown project, a psychoeducational group for guidance of parents of children, youth and adults with Down syndrome, of the PUC Goiás. We used a quantitative and qualitative research to understanding the problem studied. Using a semi-structured interview as instrument. The results show that mothers who chose the project believe that the exchange of experiences is significant and that the group also provides new friends, socialization of children, most interested in computer and after participating in the group have become confident, contributing to the development, autonomy and thus favoring the better behavior of children.Grupo Psicoeducativo de Pais: Projeto ExtensãoA Síndrome de Down na atualidade tem sido bastante discutida, porém poucas pesquisas têm se voltado para apoiar as famílias. Diante disso, este trabalho pretendeu avaliar uma ação desenvolvida no grupo psicoeducativo para pais de pessoas com síndrome down, participantes do projeto de extensão da PUC Goiás. Para tanto, o presente estudo foi de caráter quanti-qualitativo, o qual foi utilizado uma entrevista semiestruturada. Os resultados demostram que as mães ao optarem pelo projeto, entendem que a troca de experiências é significativa e que o grupo proporciona também novas amizades, socialização dos filhos, maior interesse em informática e que após participarem do grupo se tornaram empodeiradas, ou seja com maior confiança na criação dos filhos, favorecendo seu desenvolvimento pessoal, grupal e social.

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Dodangeh, Javad, Shahryar Sorooshian, and Ali Reza Afshari. "Linguistic Extension for Group Multicriteria Project Manager Selection." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/570398.

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Qualified human resource selection is one of the organizational key success factors. Since choosing the best candidate to fill the defined vacancy in a company is a complex task, intelligence analytical methods would be required to deal with this important issue. Regarding the vagueness and uncertainty of human resource selection process, it requires the linguistic extension of multicriteria decision making (MCDM) models for robust recruitment. This research is aimed to develop a fuzzy MCDM model for linguistic reasoning under new fuzzy group decision making. The new linguistic reasoning for group decision making is able to aggregate subjective evaluation of the decision makers and hence create an opportunity to perform more robust human resource selection procedures. A numerical example demonstrates possibilities for the improvement of human resource management and any other business decision areas through applying the proposed model.

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Chernet, Dawit, and K. Venkateswarlu. "On Boolean like ring extension of a group." International Journal of Algebra 8 (2014): 121–28. http://dx.doi.org/10.12988/ija.2014.312136.

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Prusińska, A., and L. Szczerba. "Geometry as an extension of the group theory." Logic and Logical Philosophy 10 (January 19, 2004): 131. http://dx.doi.org/10.12775/llp.2002.008.

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Kim, Byungsoon, and Kilwoong Jang. "Explicit Multicast Extension for a Large Multicast Group." IETE Technical Review 22, no. 3 (May 2005): 183–88. http://dx.doi.org/10.1080/02564602.2005.11657900.

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Simmross-Wattenberg, Federico, Noemí Carranza-Herrezuelo, Cristina Palacios-Camarero, Pablo Casaseca-de-la-Higuera, Miguel Ángel Martín-Fernández, Santiago Aja-Fernández, Juan Ruiz-Alzola, Carl-Fredrik Westin, and Carlos Alberola-López. "Group-Slicer: A collaborative extension of 3D-Slicer." Journal of Biomedical Informatics 38, no. 6 (December 2005): 431–42. http://dx.doi.org/10.1016/j.jbi.2005.03.001.

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Isaev, Alexei P., and Pavel Pyatov. "Spectral Extension of the Quantum Group Cotangent Bundle." Communications in Mathematical Physics 288, no. 3 (March 28, 2009): 1137–79. http://dx.doi.org/10.1007/s00220-009-0785-5.

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Lewis, Joel Brewster. "Affine symmetric group." WikiJournal of Science 4, no. 1 (2021): 3. http://dx.doi.org/10.15347/wjs/2021.003.

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The affine symmetric group is a mathematical structure that describes the symmetries of the number line and the regular triangular tesselation of the plane, as well as related higher dimensional objects. It is an infinite extension of the symmetric group, which consists of all permutations (rearrangements) of a finite set. In additition to its geometric description, the affine symmetric group may be defined as the collection of permutations of the integers (..., −2, −1, 0, 1, 2, ...) that are periodic in a certain sense, or in purely algebraic terms as a group with certain generators and relations. These different definitions allow for the extension of many important properties of the finite symmetric group to the infinite setting, and are studied as part of the fields of combinatorics and representation theory.

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Pandey, Yashonidhi. "PrincipalN-Bundles forNan Extension of a Finite Group by an Abelian Group." Communications in Algebra 39, no. 4 (March 21, 2011): 1168–80. http://dx.doi.org/10.1080/00927871003623562.

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