Results 1 to 10 of about 53,501 (261)
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
Kassabov M, Lubotzky A, Nikolov N.
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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 +2 more
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Non-simple localizations of finite simple groups
Journal of Algebra, 2006 10 ...
Jérôme Scherer +2 more
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A Characterization of the Finite Simple Groups
Journal of Algebra, 2001 The first main theorem is that if \(N\) and \(G\) are simple groups with \(|N|\) dividing \(|G|\), all indices of maximal subgroups of \(N\) being indices of maximal subgroups of \(G\), and the smallest such index being equal to the two groups, then \(N=G\) except in the two cases \((N,G)=(L_2(11),M_{11})\) and \((N,G)=(U_3(3),S_6(2))\). The proof uses
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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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Infinite locally finite simple groups with many complemented subgroups [PDF]
International Journal of Group Theory, 2022 We prove that the following families of (infinite) groups have complemented subgroup lattice: alternating groups, finitary symmetric groups, Suzuki groups over an infinite locally finite field of characteristic $2$, Ree groups over an infinite ...
Maria Ferrara, Marco Trombetti
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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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The recognition of finite simple groups with no elements of order $10$ by their element orders [PDF]
International Journal of Group Theory, 2022 The spectrum of a finite group is the set of its element orders. $H$ is said to be a finite cover of $G$ if $G$ is a homomorphic image of $H$ and $H$ is finite.
Huaiyu He, Wujie Shi
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GENERATING MAXIMAL SUBGROUPS OF FINITE ALMOST SIMPLE GROUPS
Forum of Mathematics, Sigma, 2020 For a finite group $G$, let $d(G)$ denote the minimal number of elements required to generate $G$. In this paper, we prove sharp upper bounds on $d(H)$ whenever $H$ is a maximal subgroup of a finite almost simple group.
ANDREA LUCCHINI +2 more
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A Simple Classification of Finite Groups of Order p2q2 [PDF]
Mathematics Interdisciplinary Research, 2018 Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are
Aziz Seyyed Hadi +2 more
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