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Journal articles on the topic 'Wreath product symmetry'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Dias, A. P. S., and I. Stewart. "Symmetry-Breaking Bifurcations of Wreath Product Systems." Journal of Nonlinear Science 9, no. 6 (1999): 671–95. http://dx.doi.org/10.1007/s003329900082.

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2

WOOD, DAVID. "A CAUTIONARY TALE OF COUPLING CELLS WITH INTERNAL SYMMETRIES." International Journal of Bifurcation and Chaos 11, no. 01 (2001): 123–32. http://dx.doi.org/10.1142/s0218127401001980.

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We consider the implications of "all to all" coupling of n identical, Z2 symmetric cells. In particular we demonstrate that how this coupling is achieved with respect to these internal symmetries is important, even in this very simple scenario. The coupling we consider leads to a full symmetry of Sn, Z2×Sn or Z2≀Sn, where the latter is the "wreath product" symmetry. By considering the generic solutions of each case on their respective irreducible representations, we compare and contrast the three cases, and show how very different solutions could arise in essentially similar systems.

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3

McCarthy, Patrick J. "Geometry of generalised asymptotic symmetry groups or asymptotic symmetries, product bundles and wreath products." Physics Letters A 174, no. 1-2 (1993): 25–28. http://dx.doi.org/10.1016/0375-9601(93)90536-9.

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4

Kornyak, Vladimir. "Multipartite Quantum Systems and Representations of Wreath Products." EPJ Web of Conferences 226 (2020): 02013. http://dx.doi.org/10.1051/epjconf/202022602013.

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The multipartite quantum systems are of particular interest for the study of such phenomena as entanglement and non-local correlations. The symmetry group of the whole multipartite system is the wreath product of the group acting in the “local” Hilbert space and the group of permutations of the constituents. The dimension of the Hilbert space of a multipartite system depends exponentially on the number of constituents, which leads to computational difficulties. We describe an algorithm for decomposing representations of wreath products into irreducible components. The C implementation of the a

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5

Kerber, Adalbert, and Thomas Scharf. "Tensors with icosahedral symmetry that are invariant under a certain wreath product." Journal of Mathematical Physics 28, no. 10 (1987): 2323–24. http://dx.doi.org/10.1063/1.527831.

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6

Scharf, T. "Tensors with icosahedral symmetry that are invariant under a certain wreath product. II." Journal of Physics A: Mathematical and General 22, no. 17 (1989): 3437–45. http://dx.doi.org/10.1088/0305-4470/22/17/010.

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7

Stewart, Ian, and Dinis Gökaydin. "Symmetries of Quotient Networks for Doubly Periodic Patterns on the Hexagonal Lattice." International Journal of Bifurcation and Chaos 30, no. 02 (2020): 2030004. http://dx.doi.org/10.1142/s0218127420300049.

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Pattern formation, dynamics and bifurcations for lattice models are strongly influenced by the symmetry of the lattice. However, network structure introduces additional constraints, which sometimes affect the resulting behavior. We compute the automorphism groups of all doubly periodic quotient networks of the hexagonal lattice with nearest-neighbor coupling, with emphasis on “exotic” cases where this quotient network has extra automorphisms not induced by automorphisms of the square lattice. These cases comprise three isolated networks and two infinite families with wreath product structure.

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8

Stewart, Ian, and Dinis Gökaydin. "Symmetries of Quotient Networks for Doubly Periodic Patterns on the Square Lattice." International Journal of Bifurcation and Chaos 29, no. 10 (2019): 1930026. http://dx.doi.org/10.1142/s021812741930026x.

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Patterns of synchrony in networks of coupled dynamical systems can be represented as colorings of the nodes, in which nodes of the same color are synchronous. Balanced colorings, where nodes of the same color have color-isomorphic input sets, correspond to dynamically invariant subspaces, which can have a significant effect on the typical bifurcations of network dynamical systems. Orbit colorings for subgroups of the automorphism (symmetry) group of the network are always balanced, although the converse is false. We compute the automorphism groups of all doubly periodic quotient networks of th

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9

Balasubramanian, Krishnan. "Topological Indices, Graph Spectra, Entropies, Laplacians, and Matching Polynomials of n-Dimensional Hypercubes." Symmetry 15, no. 2 (2023): 557. http://dx.doi.org/10.3390/sym15020557.

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We obtain a large number of degree and distance-based topological indices, graph and Laplacian spectra and the corresponding polynomials, entropies and matching polynomials of n-dimensional hypercubes through the use of Hadamard symmetry and recursive dynamic computational techniques. Moreover, computations are used to provide independent numerical values for the topological indices of the 11- and 12-cubes. We invoke symmetry-based recursive Hadamard transforms to obtain the graph and Laplacian spectra of nD-hypercubes and the computed numerical results are constructed for up to 23-dimensional

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10

O. J., Ben, and Auta T. J. "Determination of the Conjugacy Classes and Character Table of the Full Non-Rigid Group of Hexachlorocyclopropane Chemical Compound Via Wreath Product of Pair of Permutation Groups." African Journal of Mathematics and Statistics Studies 7, no. 1 (2024): 97–103. http://dx.doi.org/10.52589/ajmss-t9jsevag.

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The use of full non-rigid (f.NRG) molecules group theory to study the internal dynamics of molecular structures of chemical compounds is trending in the research space. In this paper, we use computational method to compute the group elements and group table of the Hexachlorocyclopropane molecular (algebraic) structure and thereafter determine the order and conjugacy classes of the group and finally the corresponding symmetry for each permutation group. We considered the point group of the compound which turns out to be isomorphic to the Wreath Products C3wrC2, where Cn denotes a cyclic group o

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11

Gribling, Sander, and Sven Polak. "Mutually unbiased bases: polynomial optimization and symmetry." Quantum 8 (April 30, 2024): 1318. http://dx.doi.org/10.22331/q-2024-04-30-1318.

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A set of k orthonormal bases of Cd is called mutually unbiased if |&#x27E8;e,f&#x27E9;|2=1/d whenever e and f are basis vectors in distinct bases. A natural question is for which pairs (d,k) there exist k mutually unbiased bases in dimension d. The (well-known) upper bound k&#x2264;d+1 is attained when d is a power of a prime. For all other dimensions it is an open problem whether the bound can be attained. Navascués, Pironio, and Acín showed how to reformulate the existence question in terms of the existence of a certain C&#x2217;-algebra. This naturally leads to a noncommutat

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12

Tout, O. "The center of the wreath product of symmetric group algebras." Algebra and Discrete Mathematics 31, no. 2 (2021): 302–22. http://dx.doi.org/10.12958/adm1338.

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We consider the wreath product of two symmetric groups as a group of blocks permutations and we study its conjugacy classes. We give a polynomiality property for the structure coefficients of the center of the wreath product of symmetric group algebras. This allows us to recover an old result of Farahat and Higman about the polynomiality of the structure coefficients of the center of the symmetric group algebra and to generalize our recent result about the polynomiality property of the structure coefficients of the center of the hyperoctahedral group algebra.

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13

Gayathri, K. S. and M. Rajeshwari∗ Mahalakshmi. "Group Actions of wreath product −→Sn on permutation groups." Scandinavian Journal of Information Systems 35, no. 1 (2023): 733–48. https://doi.org/10.5281/zenodo.7807470.

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Wreath product −→Sn = Z2 o Sn of type Bn is a subgroup of the symmetric group S2n. In this paper we determine the group actions of wreath product −→Sn on a finite set. Stabilizer and orbit of a point, imprimitivity of −→Snarealsodiscussed. Also the same is illustrated with an application for n = 3

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14

Baddeley, Robert W., Cheryl E. Praeger, and Csaba Schneider. "Transitive simple subgroups of wreath products in product action." Journal of the Australian Mathematical Society 77, no. 1 (2004): 55–72. http://dx.doi.org/10.1017/s1446788700010156.

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AbstractA transitive simple subgroup of a finite symmetric group is very rarely contained in a full wreath product in product action. All such simple permutation groups are determined in this paper. This remarkable conclusion is reached after a definition and detailed examination of ‘Cartesian decompositions’ of the permuted set, relating them to certain ‘Cartesian systems of subgroups’. These concepts, and the bijective connections between them, are explored in greater generality, with specific future applications in mind.

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15

Okada, Soichi. "Wreath products by the symmetric groups and product posets of Young's lattices." Journal of Combinatorial Theory, Series A 55, no. 1 (1990): 14–32. http://dx.doi.org/10.1016/0097-3165(90)90044-w.

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16

Dionne, Benoit, Martin Golubitsky, and Ian Stewart. "Coupled cells with internal symmetry: I. Wreath products." Nonlinearity 9, no. 2 (1996): 559–74. http://dx.doi.org/10.1088/0951-7715/9/2/016.

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17

Ganyushkin, O. G., and O. O. Desiateryk. "Automorphism groups of some variants of lattices." Carpathian Mathematical Publications 13, no. 1 (2021): 142–48. http://dx.doi.org/10.15330/cmp.13.1.142-148.

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In this paper we consider variants of the power set and the lattice of subspaces and study automorphism groups of these variants. We obtain irreducible generating sets for variants of subsets of a finite set lattice and subspaces of a finite vector space lattice. We prove that automorphism group of the variant of subsets of a finite set lattice is a wreath product of two symmetric permutation groups such as first of this groups acts on subsets. The automorphism group of the variant of the subspace of a finite vector space lattice is a natural generalization of the wreath product. The fir

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18

Kovács, L. G. "Wreath decompositions of finite permutation groups." Bulletin of the Australian Mathematical Society 40, no. 2 (1989): 255–79. http://dx.doi.org/10.1017/s0004972700004366.

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There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding ‘imprimitive wreath decomposition’ concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The result may be heuristically expressed as follows, exploiting the associative nature of the construction. Each finite transitive permutation group may be written, essentially uniquely, as the wreath produ

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19

East, James, and James Mitchell. "Generating wreath products of symmetric and alternating groups." New Zealand Journal of Mathematics 51 (December 14, 2021): 85–93. http://dx.doi.org/10.53733/108.

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20

Boyer, Robert. "Character theory of infinite wreath products." International Journal of Mathematics and Mathematical Sciences 2005, no. 9 (2005): 1365–79. http://dx.doi.org/10.1155/ijmms.2005.1365.

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The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” TheK0-invariant of the groupC∗-algebra is also determined.

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21

Gayathri, K. S., and Rajeshwari M. "CELLULAR STRUCTURE OF WREATH PRODUCT SN,USING SIGNED BRAUER DIAGRAMS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 05 (2023): 3396–409. https://doi.org/10.5281/zenodo.7932015.

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In this paper we prove that the wreath product with symmetric group <em>S<sub>n</sub>, </em>is cellular for algebra <em>Z</em><sub>2</sub>(<em>x</em>)<em>. </em>We obtain simple cell modules which satisfy semi-simplicity conditions. We make use of method of iterated inflations for this purpose.

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22

Im, Mee Seong, and Can Ozan Oğuz. "Natural Transformations between Induction and Restriction on Iterated Wreath Product of Symmetric Group of Order 2." Mathematics 10, no. 20 (2022): 3761. http://dx.doi.org/10.3390/math10203761.

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Let CAn=C[S2≀S2≀⋯≀S2] be the group algebra of an n-step iterated wreath product. We prove some structural properties of An such as their centers, centralizers, and right and double cosets. We apply these results to explicitly write down the Mackey theorem for groups An and give a partial description of the natural transformations between induction and restriction functors on the representations of the iterated wreath product tower by computing certain hom spaces of the category of ⨁m≥0(Am,An)−bimodules. A complete description of the category is an open problem.

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23

ŚNIADY, PIOTR. "GAUSSIAN FLUCTUATIONS OF REPRESENTATIONS OF WREATH PRODUCTS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 09, no. 04 (2006): 529–46. http://dx.doi.org/10.1142/s0219025706002524.

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We study the asymptotics of the reducible representations of the wreath products G≀Sq = Gq ⋊ Sq for large q, where G is a fixed finite group and Sq is the symmetric group in q elements; in particular for G = ℤ/2ℤ we recover the hyperoctahedral groups. We decompose such a reducible representation of G≀Sq as a sum of irreducible components (or, equivalently, as a collection of tuples of Young diagrams) and we ask what is the character of a randomly chosen component (or, what are the shapes of Young diagrams in a randomly chosen tuple). Our main result is that for a large class of representations

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24

Sinchuk, S. "Parametrized symmetric groups and the second homology of a group." St. Petersburg Mathematical Journal 32, no. 6 (2021): 1067–80. http://dx.doi.org/10.1090/spmj/1685.

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The notion of a symmetric group parametrized by elements of a group is introduced. It is shown that this group is an extension of a subgroup of the wreath product G ≀ S n G \wr S_n by H 2 ⁡ ( G , Z ) \operatorname {H}_2(G, \mathbb {Z}) . Motivation behind this construction is also discussed.

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25

Green, Reuben. "Specht module branching rules for wreath products of symmetric groups." Algebraic Combinatorics 5, no. 4 (2022): 609–28. http://dx.doi.org/10.5802/alco.223.

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26

Kitaev, Sergey, Andrew Niedermaier, Jeffrey Remmel, and Manda Riehl. "Generalized Pattern-Matching Conditions for." ISRN Combinatorics 2013 (February 13, 2013): 1–20. http://dx.doi.org/10.1155/2013/634823.

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We derive several multivariable generating functions for a generalized pattern-matching condition on the wreath product of the cyclic group and the symmetric group . In particular, we derive the generating functions for the number of matches that occur in elements of for any pattern of length 2 by applying appropriate homomorphisms from the ring of symmetric functions over an infinite number of variables to simple symmetric function identities. This allows us to derive several natural analogues of the distribution of rises relative to the product order on elements of . Our research leads to co

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27

Law, Maska, Alice C. Niemeyer, Cheryl E. Praeger, and Ákos Seress. "A Reduction Algorithm for Large-Base Primitive Permutation Groups." LMS Journal of Computation and Mathematics 9 (2006): 159–73. http://dx.doi.org/10.1112/s1461157000001236.

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AbstractThe authors present a nearly linear-time Las Vegas algorithm that, given a large-base primitive permutation group, constructs its natural imprimitive representation. A large-base primitive permutation group is a subgroup of a wreath product of symmetric groups Sn and Sr in product action on r-tuples of k-element subsets of {1, …, n}, containing Anr. The algorithm is a randomised speed-up of a deterministic algorithm of Babai, Luks, and Seress.

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Kitaev, Sergey, Jeffrey Remmel, and Manda Riehl. "Generalized Pattern Avoidance Condition for the Wreath Product of Cyclic Groups with Symmetric Groups." ISRN Combinatorics 2013 (January 17, 2013): 1–17. http://dx.doi.org/10.1155/2013/806583.

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We continue the study of the generalized pattern avoidance condition for Ck≀Sn, the wreath product of the cyclic group Ck with the symmetric group Sn, initiated in the work by Kitaev et al., In press. Among our results, there are a number of (multivariable) generating functions both for consecutive and nonconsecutive patterns, as well as a bijective proof for a new sequence counted by the Catalan numbers.

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29

CHUANG, JOSEPH, and RADHA KESSAR. "SYMMETRIC GROUPS, WREATH PRODUCTS, MORITA EQUIVALENCES, AND BROUÉ'S ABELIAN DEFECT GROUP CONJECTURE." Bulletin of the London Mathematical Society 34, no. 2 (2002): 174–85. http://dx.doi.org/10.1112/s0024609301008839.

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It is shown that for any prime p, and any non-negative integer w less than p, there exist p-blocks of symmetric groups of defect w, which are Morita equivalent to the principal p-block of the group Sp [rmoust ] Sw. Combined with work of J. Rickard, this proves that Broué's abelian defect group conjecture holds for p-blocks of symmetric groups of defect at most 5.

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30

WOESS, WOLFGANG. "A NOTE ON THE NORMS OF TRANSITION OPERATORS ON LAMPLIGHTER GRAPHS AND GROUPS." International Journal of Algebra and Computation 15, no. 05n06 (2005): 1261–72. http://dx.doi.org/10.1142/s0218196705002591.

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Let L≀X be a lamplighter graph, i.e., the graph-analogue of a wreath product of groups, and let P be the transition operator (matrix) of a random walk on that structure. We explain how methods developed by Saloff-Coste and the author can be applied for determining the ℓp-norms and spectral radii of P, if one has an amenable (not necessarily discrete or unimodular) locally compact group of isometries that acts transitively on L. This applies, in particular, to wreath products K≀G of finitely-generated groups, where K is amenable. As a special case, this comprises a result of Żuk regarding the ℓ

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31

Cedric, Pemha Binyam Gabriel. "A linear portrayal of the Galois group G by the ring of irreducible characters of the hyperoctahedral group." Journal of Discrete Mathematical Sciences and Cryptography 28, no. 3 (2025): 701–13. https://doi.org/10.47974/jdmsc-1858.

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The purpose of this paper is to first present the hyperoctahedral group, Bn, as the wreath product of ℤ2 associated with Sn, the symmetric group and then from the ring, A, generated by the irreducible characters of Bn define a linear portrayal of Artin attached to L/K; K is the field associated with the corresponding valuation ring AK issued from A.

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32

Hemalatha, P., and A. Muthusamy. "Evenly partite star factorization of symmetric digraph of wreath product of graphs." AKCE International Journal of Graphs and Combinatorics 14, no. 1 (2017): 54–62. http://dx.doi.org/10.1016/j.akcej.2016.11.002.

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33

JONES, G. A., and K. D. SOOMRO. "THE MAXIMALITY OF CERTAIN WREATH PRODUCTS IN ALTERNATING AND SYMMETRIC GROUPS." Quarterly Journal of Mathematics 37, no. 4 (1986): 419–35. http://dx.doi.org/10.1093/qmath/37.4.419.

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34

OHMOTO, TORU. "Generating functions of orbifold Chern classes I: symmetric products." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 2 (2008): 423–38. http://dx.doi.org/10.1017/s0305004107000898.

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AbstractIn this paper, for a possibly singular complex variety X, generating functions of total orbifold Chern homology classes of the symmetric products SnX are given. These are very natural “class versions” of known generating function formulae of (generalized) orbifold Euler characteristics of SnX. Our Chern classes work covariantly for proper morphisms. We state the result more generally. Let G be a finite group and Gn the wreath product G ∼ Sn. For a G-variety X and a group A, we show a “Dey–Wohlfahrt type formula“ for equivariant Chern–Schwartz–MacPherson classes associated to Gn-represe

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35

KLÜNERS, JÜRGEN. "THE DISTRIBUTION OF NUMBER FIELDS WITH WREATH PRODUCTS AS GALOIS GROUPS." International Journal of Number Theory 08, no. 03 (2012): 845–58. http://dx.doi.org/10.1142/s1793042112500492.

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Let G be a wreath product of the form C2 ≀ H, where C2 is the cyclic group of order 2. Under mild conditions for H we determine the asymptotic behavior of the counting functions for number fields K/k with Galois group G and bounded discriminant. Those counting functions grow linearly with the norm of the discriminant and this result coincides with a conjecture of Malle. Up to a constant factor these groups have the same asymptotic behavior as the conjectured one for symmetric groups.

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36

Hemalatha, P., and A. Muthusamy. "$\widetilde{S}_k$-Factorization of the symmetric digraph of wreath product of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (2014): 1450048. http://dx.doi.org/10.1142/s1793830914500487.

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In this paper, we show that the necessary and sufficient condition for the existence of an [Formula: see text]-factorization of [Formula: see text] is n ≡ 0 ( mod k(k - 1)), for all m > 3. In fact, our result together with a result of Ushio gives a complete solution for the existence of an [Formula: see text]-factorization of [Formula: see text] for all m ≥ 3. Further, we have obtained some necessary or sufficient conditions for the existence of an [Formula: see text]-factorization of [Formula: see text], for all even k ≥ 4 and m > 3.

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37

Novelli, Jean-Christophe, and Jean-Yves Thibon. "Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions." Discrete Mathematics 310, no. 24 (2010): 3584–606. http://dx.doi.org/10.1016/j.disc.2010.09.008.

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38

IMAOKA, TERUO, ISAMU INATA, and HIROAKI YOKOYAMA. "REPRESENTATIONS OF LOCALLY INVERSE *-SEMIGROUPS." International Journal of Algebra and Computation 06, no. 05 (1996): 541–51. http://dx.doi.org/10.1142/s0218196796000295.

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The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *-semigroup on a π-set, and show that any locally inverse *-semigroup can be embedded up to *-isomorphism in the π-symmetric locally inverse semigroup on a π-set. Moreover, we shall obtain that the wreath product of locally inverse *-semigroups is

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39

Hirai, Takeshi, and Etsuko Hirai. "Characters of wreath products of finite groups with the infinite symmetric group." Journal of Mathematics of Kyoto University 45, no. 3 (2005): 547–97. http://dx.doi.org/10.1215/kjm/1250281973.

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40

Poulain d’Andecy, L. "Fusion Procedure for Wreath Products of Finite Groups by the Symmetric Group." Algebras and Representation Theory 17, no. 3 (2013): 809–30. http://dx.doi.org/10.1007/s10468-013-9419-x.

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41

Nonkané, Ibrahim, and Latevi Lawson. "Invariant differential operators and the generalized symmetric group." Gulf Journal of Mathematics 13, no. 2 (2022): 19–32. http://dx.doi.org/10.56947/gjom.v13i2.738.

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In this paper we study the decomposition of the direct image of π+(OX) the polynomial ring OX as a D-module, under the map π: spec OX →spec OXG(r,n), where OXG(r,n) is the ring of invariant polynomial under the action of the wreath product G(r, p):= Z/rZ ~Sn. We first describe the generators of the simple components of π+(OX) and give their multiplicities. Using an equivalence of categories and the higher Specht polynomials, we describe a D-module decomposition of the polynomial ring localized at the discriminant of π. Furthermore, we study the action invariants, differential operators, on the

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42

Wagner, Jennifer D. "The permutation enumeration of wreath products Ck§Sn of cyclic and symmetric groups." Advances in Applied Mathematics 30, no. 1-2 (2003): 343–68. http://dx.doi.org/10.1016/s0196-8858(02)00539-0.

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43

Pushkarev, I. A. "On the representation theory of wreath products of finite groups and symmetric groups." Journal of Mathematical Sciences 96, no. 5 (1999): 3590–99. http://dx.doi.org/10.1007/bf02175835.

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44

KOCHUBINSKA, YEVGENIYA. "ON ISOMORPHISMS OF $\mathcal{R}$- AND $\mathcal{L}$-CROSS-SECTIONS OF WREATH PRODUCTS OF FINITE INVERSE SYMMETRIC SEMIGROUPS." International Journal of Algebra and Computation 19, no. 08 (2009): 999–1010. http://dx.doi.org/10.1142/s0218196709005469.

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We classify [Formula: see text]- and [Formula: see text]-cross-sections of wreath products of finite inverse symmetric semigroups [Formula: see text] up to isomorphism. We show that every isomorphism of [Formula: see text] cross-sections of [Formula: see text] is a conjugacy. As an auxiliary result, we get that every isomorphism of [Formula: see text] cross-sections of [Formula: see text] is also a conjugacy. We also compute the number of non-isomorphic [Formula: see text] cross-sections of [Formula: see text].

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45

Combariza, German, Juan Rodriguez, and Mario Velasquez. "Induced character in equivariant K-theory, wreath products and pullback of groups." Revista Colombiana de Matemáticas 56, no. 1 (2022): 35–61. http://dx.doi.org/10.15446/recolma.v56n1.105613.

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Let G be a finite group and let X be a compact G-space. In this note we study the (Z+ × Z/2Z)-graded algebra FqG (X) = ⊕n ≤ 0 qn · KG∫Gn(Xn) ⊗ C, defined in terms of equivariant K-theory with respect to wreath products as a symmetric algebra, we review some properties of FqG (X) proved by Segal and Wang. We prove a Kunneth type formula for this graded algebras, more specifically, let H be another finite group and let Y be a compact H-space, we give a decomposition of FqG × H (X × Y) in terms of FqG (X) and FqH (Y). For this, we need to study the representation theory of pullbacks o

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Madani, Somayeh, and Ali Reza Ashraf. "General form of the automorphism group of bicyclic graphs." Quasigroups and Related Systems 31, no. 1(49) (2023): 97–116. http://dx.doi.org/10.56415/qrs.v31.07.

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In 1869, Jordan proved that the set T of all finite groups that can be represented as the automorphism group of a tree is containing the trivial group, it is closed under taken the direct product of groups of lower orders in T , and wreath product of a member of T and the symmetric group on n symbols is again an element of T . The aim of this paper is to continue this work and another works by Klavik and Zeman in 2017 to present a class S of finite groups for which the automorphism group of each bicyclic graph is a member of S and this class is minimal with this property.

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Benson, David J. "ON THE REGULARITY CONJECTURE FOR THE COHOMOLOGY OF FINITE GROUPS." Proceedings of the Edinburgh Mathematical Society 51, no. 2 (2008): 273–84. http://dx.doi.org/10.1017/s0013091505001203.

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AbstractLet $K$ be a field of characteristic $p$ and let $G$ be a finite group of order divisible by $p$. The regularity conjecture states that the Castelnuovo–Mumford regularity of the cohomology ring $H^*(G,K)$ is always equal to 0. We prove that if the regularity conjecture holds for a finite group $H$, then it holds for the wreath product $H\wr\mathbb{Z}/p$. As a corollary, we prove the regularity conjecture for the symmetric groups $\varSigma_n$. The significance of this is that it is the first set of examples for which the regularity conjecture has been checked, where the difference betw

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Akazawa, Hiroki, and Hiroshi Mizukawa. "Orthogonal polynomials arising from the wreath products of a dihedral group with a symmetric group." Journal of Combinatorial Theory, Series A 104, no. 2 (2003): 371–80. http://dx.doi.org/10.1016/j.jcta.2003.09.001.

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Gramain, Jean-Baptiste, and Adriana Marciuk. "Restriction of characters to subgroups of wreath products and basic sets for the symmetric group." Communications in Algebra 48, no. 6 (2020): 2428–41. http://dx.doi.org/10.1080/00927872.2020.1714638.

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Fripertinger, Harald. "On Iteration of Bijective Functions with Discontinuities." Annales Mathematicae Silesianae 34, no. 1 (2020): 51–72. http://dx.doi.org/10.2478/amsil-2020-0009.

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AbstractWe present three different types of bijective functions f : I → I on a compact interval I with finitely many discontinuities where certain iterates of these functions will be continuous. All these examples are strongly related to permutations, in particular to derangements in the first case, and permutations with a certain number of successions (or small ascents) in the second case. All functions of type III form a direct product of a symmetric group with a wreath product. It will be shown that any iterative root F : J → J of the identity of order k on a compact interval J with finitel

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