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Chiral polyhedra and finite simple groups [PDF]
, 2016 We prove that every finite non‐abelian simple group acts as the automorphism group of a chiral polyhedron, apart from the groups PSL2(q) , PSL3(q) , PSU3(q) and A7 .
D. Leemans, M. Liebeck
semanticscholar +1 more source
Products of conjugacy classes and fixed point spaces [PDF]
, 2011 We prove several results on products of conjugacy classes in finite simple groups. The first result is that there always exists a uniform generating triple.
Guralnick, Robert, Malle, Gunter
core
Area preserving group actions on surfaces
, 2003 Suppose G is an almost simple group containing a subgroup isomorphic to the three-dimensional integer Heisenberg group. For example any finite index subgroup of SL(3,Z) is such a group.
Casson +13 more
core +1 more source
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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Large subgroups of simple groups
, 2014 Let $G$ be a finite group. A proper subgroup $H$ of $G$ is said to be large if the order of $H$ satisfies the bound $|H|^3 \ge |G|$. In this note we determine all the large maximal subgroups of finite simple groups, and we establish an analogous result ...
Alavi, S. Hassan, Burness, Timothy C.
core +1 more source
Probabilistic Generation of Finite Simple Groups
Journal of Algebra, 2000 It is well known that any finite group \(G\) can be generated by two elements and the probability that two elements generate \(G\) approaches 1 as the order of \(G\) goes to infinity. The paper under review deals with a more specific problem. As the main result the authors prove that for each finite almost simple group \(G\) there exists a conjugacy ...
Guralnick, Robert M., Kantor, William M.
openaire +1 more source
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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Simple groups admit Beauville structures
, 2011 We answer a conjecture of Bauer, Catanese and Grunewald showing that all finite simple groups other than the alternating group of degree 5 admit unmixed Beauville structures.
Guralnick, Robert, Malle, Gunter
core +1 more source
Random Generation of Finite Simple Groups
Journal of Algebra, 1999 \textit{J. D. Dixon} [Math. Z. 110, 199-205 (1969; Zbl 0176.29901)] conjectured that if two elements are randomly chosen from a finite simple group \(G\), they will generate \(G\) with probability \(\to 1\) as \(|G|\to\infty\). Dixon [ibid.] proved this if \(G\) is an alternating group. \textit{W. M. Kantor} and \textit{A. Lubotzky} [Geom. Dedicata 36,
Guralnick, Robert M. +3 more
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On a New Criterion for the Solvability of Non-Simple Finite Groups and m-Abelian Solvability [PDF]
, 2021 Hasan Sankari, Mohammad Abobala
openalex +1 more source