Simple groups, permutation groups, and probability

Liebeck, Martin¹ ; Shalev, Aner²

¹ Department of Mathematics, Imperial College, London SW7 2BZ, England
² Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel

Journal of the American Mathematical Society, Tome 12 (1999) no. 2, pp. 497-520

Résumé

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.

Détail

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

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