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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.
M A Grechkoseeva +2 more
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Non-simple localizations of finite simple groups
Journal of Algebra, 2006 10 ...
JOSÉ L Rodríguez +2 more
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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.
europepmc +5 more sources
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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Divisibility and laws in finite simple groups [PDF]
Mathematische Annalen, 2015 20 pages, no figures; v3 completely rewritten with new co-author and new ...
Gady Kozma, Andreas Thom
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Products of squares in finite simple groups [PDF]
Proceedings of the American Mathematical Society, 2011 The Ore conjecture, proved by the authors, states that every element of every finite non-abelian simple group is a commutator. In this paper we use similar methods to prove that every element of every finite simple group is a product of two squares. This can be viewed as a non-commutative analogue of Lagrange’s four squares theorem.
Liebeck, Martin W. +3 more
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On the minimal dimension of a finite simple group [PDF]
Journal of Combinatorial Theory, Series A, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Timothy C. Burness +2 more
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On the structure of finite groups isospectral to finite simple groups [PDF]
Journal of Group Theory, 2015 Abstract Finite groups are said to be isospectral if they have the same sets of element orders. A finite nonabelian simple group L is said to be almost recognizable by spectrum if every finite group isospectral to L is an almost simple group with socle isomorphic to L.
Grechkoseeva, Mariya A. +1 more
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The Waring problem for finite simple groups [PDF]
Annals of Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Larsen, Aner Shalev, Pham Tiep
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Centralisers of finite groups in locally finite simple groups
Communications in Algebra, 2023 10 ...
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