Results 1 to 10 of about 1,671,117 (167)
ON THE GENERATING GRAPH OF A SIMPLE GROUP [PDF]
Journal of the Australian Mathematical Society, 2016 The generating graph $\unicode[STIX]{x1D6E4}(H)$ of a finite group $H$ is the graph defined on the elements of $H$, with an edge between two vertices if and only if they generate $H$. We show that if $H$ is a sufficiently large simple group with $\unicode[STIX]{x1D6E4}(G)\cong \unicode[STIX]{x1D6E4}(H)$ for a finite group $G$, then $G\cong H$.
LUCCHINI, ANDREA +2 more
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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 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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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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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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Journal of Algebra, 2001 A finite simple group \(G\) is called simple \(K_n\)-group if the order of \(G\) has exactly \(n\) distinct prime factors. It is well known that the number of simple \(K_3\)-groups is eight [\textit{M. Herzog}, J. Algebra 10, 383-388 (1968; Zbl 0167.29101)].
Bugeaud, Yann +2 more
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Torsion units in integral group ring of the Mathieu simple group M22 [PDF]
, 2008 We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group M22.
Bódi, Viktor +6 more
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ON THE PRIME GRAPH OF SIMPLE GROUPS [PDF]
Bulletin of the Australian Mathematical Society, 2014 AbstractLet $G$ be a finite group, let ${\it\pi}(G)$ be the set of prime divisors of $|G|$ and let ${\rm\Gamma}(G)$ be the prime graph of $G$. This graph has vertex set ${\it\pi}(G)$, and two vertices $r$ and $s$ are adjacent if and only if $G$ contains an element of order $rs$.
Burness, Tim C, Covato, Elisa
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Graphs related to Held's simple group [PDF]
, 1989 We analyze the permutation representations of low degree of Held's simple group He. We also determine its primitive multiplicity free permutation representations and show that there is no graph on which it or its automorphism group acts as a distance ...
Cuypers, F.G.M.T. +16 more
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Finite simple groups as expanders [PDF]
Proceedings of the National Academy of Sciences, 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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