Probabilistic generation of finite simple groups, II

By T. Breuer, Robert M. Guralnick, William M. Kantor. 2000

156 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Discrete Mathematics and Combinatorics, Genetics

View Paper: https://www.semanticscholar.org/paper/cd3bfcc31f0f6ec97ee02dd0355ee4a2809b061f

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In Computer Networks and Communications

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Citations in the corpus

Derangements in simple and primitive groups (2002, background): “If G is a finite simple group, set PG(x) the probability that a random y ∈ G satisfies G = h x, yi . Let PG be the minimum of PG(x) over all nontrivial x. It follows by [ GK ] that PG > 0. One can easily deduce the following result (a special case of [GLSS]):”
Diameters of finite simple groups: sharp bounds and applications (2001, background): “12 joins a growing number of recent results on random generation of finite simple groups (see for instance [17], [23], [24], [25], [12], [11], [13]).”
Graphs defined on groups (2021, methodology): “The generating graph was introduced in [76], and studied further in [27].”
Fixed point ratios in actions of finite classical groups, III (2007, background): “In recent years, a number of papers have appeared where bounds on fixed point ratios for actions of simple groups are obtained and then applied to a number of dierent problems, see [11, 12, 13, 14 , 17, 20] for example.”
WHAT DO WE KNOW ABOUT THE PRODUCT REPLACEMENT ALGORITHM (2009, unknown): “Theorem 1.1.8 ([ GK ]) Let G be a nonabelian nite simple group.”
On fixed points of permutations (2007, unknown): “This fact has been usefully applied in quite a few papers (see [ GKa ], [FG4] and the references therein, for example).”
The spread of a finite group (2020, methodology): “Since the theorem for simple exceptional groups is proved in [10], we will always assume that G is almost simple, but not simple.”
Fixed point ratios in actions of finite exceptional groups of lie type. (2002, background): “We refer the reader in particular to [23, 27, 30, 52], where upper bounds on fixed point ratios are obtained and applied to various problems when G is a classical group; to [42], where a general upper bound of 4/3q is obtained for groups of Lie type over Fq (with a few exceptions); and to [24, 52], ”