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Simple groups contain minimal simple groups [PDF]
Publicacions Matemàtiques, 1997 It is a consequence of the classification of finite simple groups that every non-abelian simple group contains a subgroup which is a minimal simple group.
Barry, M. J. J., Ward, M. B.
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Finite simple groups as expanders. [PDF]
Proc Natl Acad Sci U S A, 2006 We prove that there exist k ∈ ℕ and 0 < ε ∈ ℝ such that every non-abelian finite simple group G , which is not a Suzuki group, has a set of k generators for which the Cayley graph Cay( G ; S ) is an ε-expander.
Kassabov M, Lubotzky A, Nikolov N.
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Representations of extensions of simple groups. [PDF]
Arch MathAbstract Feit and Tits (1978) proved that a nontrivial projective representation of minimal dimension of a finite extension of a finite nonabelian simple group G factors through a projective representation of G, except for some groups of Lie type in characteristic 2; the exact exceptions for G were determined by Kleidman and Liebeck (1989 ...
Harper S, Liebeck MW.
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Alperin weight conjecture and related developments
Bulletin of Mathematical Sciences, 2022 The Alperin weight conjecture is central to the modern representation theory of finite groups, and it is still open, despite many different approaches from different points of view.
Zhicheng Feng, Jiping Zhang
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Finite groups whose maximal subgroups of even order are MSN-groups
Open Mathematics, 2022 A finite group GG is called an MSN-group if all maximal subgroups of the Sylow subgroups of GG are subnormal in GG. In this article, we investigate the structure of finite groups GG such that GG is a non-MSN-group of even order in which every maximal ...
Wang Wanlin, Guo Pengfei
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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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A new characterization of some characteristically simple groups [PDF]
AUT Journal of Mathematics and Computing, 2023 Let $G$ be a finite group and $\mathrm{cd}(G)$ be the set of irreducible complex character degrees of $G$. It was proved that some finite simple groups are uniquely determined by their orders and their degree graphs.
Zohreh Sayanjali
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Finite Groups Isospectral to Simple Groups
Communications in Mathematics and Statistics, 2022 The spectrum of a finite group is the set of element orders of this group. The main goal of this paper is to survey results concerning recognition of finite simple groups by spectrum, in particular, to list all finite simple groups for which the recognition problem is solved.
Maria A. Grechkoseeva +4 more
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On a conjecture on simple groups [PDF]
Proceedings of the American Mathematical Society, 1950 The purpose of this paper is to rephrase a conjecture about simple groups into the language of linear algebra. Let G be a group of finite order o(G). Then by rF we shall mean the group ring of G over a field of characteristic p (for instance the integers modulo p). We shall denote the radical of rF by N,. If p = 0 or p o(G), then it is known that Np=(O)
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Siberian Mathematical Journal, 2014 The main aim of this article is to establish a classification of simple polyadic groups in terms of ordinary groups and their automorphisms. We give two different definitions of simpleness for polyadic groups, from the point of views of universal algebra, UAS (universal algebraically simpleness), and group theory, GTS (group theoretically simpleness ...
Khodabandeh, H., Shahryari, M.
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