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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
Strong reality of finite simple groups [PDF]
Siberian Mathematical Journal, 2010 The classification of finite simple strongly real groups is complete. It is easy to see that strong reality for every nonabelian finite simple group is equivalent to the fact that each element can be written as a product of two involutions.
Gal't, A. A., Vdovin, E. P.
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Beauville surfaces and finite simple groups [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2010 A Beauville surface is a rigid complex surface of the form (C1 x C2)/G, where C1 and C2 are non-singular, projective, higher genus curves, and G is a finite group acting freely on the product.
Alexander Lubotzky +5 more
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Simple Finite Non-Abelian Flavor Groups [PDF]
Journal of Mathematical Physics, 2007 The recently measured unexpected neutrino mixing patterns have caused a resurgence of interest in the study of finite flavor groups with two- and three-dimensional irreducible representations.
Christoph Luhn +4 more
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Infinite products of finite simple groups [PDF]
Transactions of the American Mathematical Society, 1996 We classify those sequences $\langle S_{n} \mid n \in \mathbb{N} \rangle$ of finite simple nonabelian groups such that the full product $\prod_{n} S_{n}$ has property (FA).Comment: AMS-LaTex file, 44 pages. To appear in Tran. Amer.
Saxl, Jan +2 more
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Fuchsian groups, finite simple groups and representation varieties [PDF]
Inventiones mathematicae, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liebeck, MW, Shalev, A
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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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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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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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