Colin will try to show the following: let G be a finite group such that p is the largest prime dividing the order of G, and every Sylow subgroup of G is generated by at most d elements. Then G has a nilpotent normal subgroup of index bounded by a function of p and d. (In this context, nilpotent means a direct product of groups of prime power order.) In particular, there are only finitely many primitive groups with these parameters. He will explain the group theory terminology at the start for those who are unfamiliar with it.
Finite groups whose Sylow subgroups have a bounded number of generators
Wed, 03/02/2010 - 12:05