Simple groups, permutation groups, and probability |
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| Authors: | Martin W. Liebeck Aner Shalev |
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| Affiliation: | Department of Mathematics, Imperial College, London SW7 2BZ, England ; Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel |
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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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