Simple groups, permutation groups, and probability

Liebeck, Martin; Shalev, Aner

doi:10.1090/S0894-0347-99-00288-X

Simple groups, permutation groups, and probability
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by Martin W. Liebeck and Aner Shalev

J. Amer. Math. Soc. 12 (1999), 497-520

DOI: https://doi.org/10.1090/S0894-0347-99-00288-X

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Abstract:

We derive a new bound for the minimal degree of an almost simple primitive permutation group, and settle a conjecture of Cameron and Kantor concerning the base size of such a group. Additional results concern random generation of simple groups, and the so-called genus conjecture of Guralnick and Thompson. Our proofs are based on probabilistic arguments, together with a new result concerning the size of the intersection of a maximal subgroup of a classical group with a conjugacy class of elements.

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