Simple groups, permutation groups, and probability
J. Amer. Math. Soc. 12 (1999), 497-520.
Martin W. Liebeck 
Department of Mathematics, Imperial College, London SW7 2BZ, England 
and Aner Shalev
Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel 

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.