In this paper we obtain a classification of those subgroups of the finite general linear group GLd (q) with orders divisible by a primitive prime divisor of qe − 1 for some . In the course of the… Expand

We show that random Cayley graphs of finite simple (or semisimple) groups of Lie type of fixed rank are expanders. The proofs are based on the Bourgain-Gamburd method and on the main result of our… Expand

Let G be a finite almost simple group, with L = F ∗(G) the unique minimal norma subgroup ofG—soL is a finite simple group. For x ∈G, letα(x) be the minimal numbe of L-conjugates of x which generate… Expand

We present explicit upper bounds for the number and size of conjugacy classes in finite Chevalley groups and their variations. These results have been used by many authors to study zeta functions… Expand

Abstract We improve a result of Liebeck and Saxl concerning the minimal degree of a primitive permutation group and use it to strengthen a result of Guralnick and Neubauer on generic covers of… Expand

For Bernd Fischer on the occasion of his 70th birthdayIntroduction: When Gis a nite group, we may endow G Gwith the structureof a probability space by assigning the uniform distribution. As was… Expand