Results 1 to 10 of about 6,235 (209)
On conjugacy classes in groups [PDF]
Journal of Algebra, 2023 Let $G$ be a group. Write $G^{*}=G\setminus \{1\}$.
M. Herzog, P. Longobardi, M. Maj
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Squares of real conjugacy classes in finite groups [PDF]
Annali Di Matematica Pura Ed Applicata, 2017 We prove that if a finite group G contains a conjugacy class K whose square is of the form 1∪D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs ...
Antonio Beltran
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Cryptanalysis of some nonabelian group-based key exchange protocols [PDF]
Journal of Mathematical CryptologyIn the recently emerging field of nonabelian group-based cryptography, a prominently used one-way function is the conjugacy search problem (CSP), and two important classes of platform groups are polycyclic and matrix groups. In this paper, we discuss the
Tinani Simran +2 more
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Multicomponent KP type hierarchies and their reductions, associated to conjugacy classes of Weyl groups of classical Lie algebras [PDF]
Journal of Mathematics and Physics, 2023 This, to a large extent, expository paper describes the theory of multicomponent hierarchies of evolution equations of XKP type, where X = A, B, C, or D, and AKP = KP and their reductions, associated with the conjugacy classes of the Weyl groups of ...
V. Kac, J. van de Leur
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Conjugacy classes of big mapping class groups [PDF]
Journal of the London Mathematical Society, 2021 We describe the topological behavior of the conjugacy action of the mapping class group of an orientable infinite‐type surface Σ$\Sigma$ on itself by proving that: (1)all conjugacy classes of Map(Σ)$\operatorname{Map}(\Sigma )$ are meager for every Σ ...
Jesús Hernández Hernández +5 more
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New lower bounds for the number of conjugacy classes in finite nilpotent groups [PDF]
International Journal of Group Theory, 2022 P. Hall's classical equality for the number of conjugacy classes in $p$-groups yields $k(G) \ge (3/2) \log_2 |G|$ when $G$ is nilpotent. Using only Hall's theorem, this is the best one can do when $|G| = 2^n$. Using a result of G.J.
Edward A. Bertram
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Reality Properties of Finite Simple Orthogonal Groups [PDF]
Advances in Group Theory and Applications, 2023 We prove several reality properties for finite simple orthogonal groups. For any prime power q and m ≥ 1, we show that all real conjugacy classes are strongly real in the simple groups PΩ±(4m + 2, q), m ≥ 1, except in the case PΩ−(4m + 2, q) with q ≡ 3 ...
J. Kim, S. Trefethen, C.R. Vinroot
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Conjugacy classes contained in normal subgroups: an overview [PDF]
International Journal of Group Theory, 2018 We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group.
Antonio Beltran +2 more
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On the Regular Power Graph on the Conjugacy Classes of Finite Groups [PDF]
Mathematics Interdisciplinary Research, 2018 The (undirected) power graph on the conjugacy classes PC(G) of a group G is a simple graph in which the vertices are the conjugacy classes of G and two distinct vertices C and C' are adjacent in PC(G) if one is a subset of a power of the other.
Sajjad Mahmood Robati
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Twisted conjugacy in direct products of groups [PDF]
Communications in Algebra, 2021 Given a group G and an endomorphism of G, two elements are said to be -conjugate if for some The number of equivalence classes for this relation is the Reidemeister number of The set is called the Reidemeister spectrum of G.
Pieter Senden
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