Breadcrumb
Generation and random generation of simple groups and their subgroups
Wed 20 February 2013, 14:30
Tim Burness
University of Southampton
Organisers: Tony Skyner, Neil Saunders
ABSTRACT
Let G be a finite group and let d(G) be the minimal number of generators for G. For example, it is well known that d(G) = 2 for every nonabelian finite simple group G. A wide range of generation properties for simple groups has been studied in recent years, using detailed information on the subgroup structure of these groups. I will briefly recall some of the main results, and I will report on recent joint work with Martin Liebeck and Aner Shalev on the generation of maximal subgroups of simple groups. Applications to second maximal subgroups and primitive permutation groups will also be discussed.