SEMINAR: Groups and Combinatorics Seminar: Symmetric p-groups

Alice Niemeyer (UWA)

will speak on

Symmetric p-groups

at 11am in Weatherburn LT

(The time will be finalised on Wed evening. There may be the need for a change of time to 1:30pm.)

Abstract: In 1978 R.M. Bryant and L.G. Kov acs showed that for every subgroup H of GL(d,p) for a prime p there is a finite p-group P such that the automorphism group of P induces a subgroup on the Frattini quotient P/ hi(P) which is isomorphic to H. Their proof demonstrates the existence of such a p-group by considering sufficiently large quotients to terms of the exponent-p lower central series of the free group F on d generators.

In joint work with J. Bamberg, S. Glasby and L. Morgan we consider maximal subgroups of GL(d,p) for odd primes p and d at least 4 and show that in many cases we only need to consider the exponent-p lower central series of F of class 3 to find such a p-group.