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Linear Groups with Orders Having Certain Large Prime Divisors
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 theExpand
Expansion in finite simple groups of Lie type
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 ourExpand
Generation of finite almost simple groups by conjugates
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 generateExpand
Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements
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 functionsExpand
On the Minimal Degree of a Primitive Permutation Group
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 ofExpand
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 wasExpand