SEMINAR: Groups and Combinatorics Seminar, Generalized quadrangles and AS-configurations of finite p-groups

Stephen Glasby (UWA)

will speak on

Generalized quadrangles and AS-configurations of finite p-groups

at 3pm Friday 12 September in Weatherburn Lecture Theatre.

Abstract:

This is joint work with John Bamberg and Eric Swartz at UWA. One method for constructing generalized quadrangles involves finding a certain family of subgroups of a group. Given a group G of order q^3 we seek a family of q+2 subgroups U_0, U_1,..., U_{q+1} of G, each of order q, such that U_0 is normal in G and U_iU_j ap U_k={1} for all distinct i,j,k in {0,1,...,q+1}. The family is called an AS-configuration for G. We determine all the AS-configurations for q odd as well as q=2,4,8. To determine q=8 we showed, using extensive theory and computation, that only one of the 10,494,213 groups of order 2^9 admits an AS-configuration!