SEMINAR: Groups and Combinatorics Seminar: Fat elements in the sporadic simple groups and their covering groups

Groups and Combinatorics Seminar

Sabina Pannek (UWA/Aachen)

will speak on

Fat elements in the sporadic simple groups and their covering groups.

at 1pm on Tuesday 26th of October in MLR2

Abstract: Consider the finite general linear group G = GL(d,q) with d > 2. We call an element of G fat, or more precisely a fat(d,q;e)-element, if it leaves invariant and acts irreducibly on a subspace of dimension e > d/2. Equivalently, g in G is a fat(d,q;e)-element if the characteristic polynomial for g has an irreducible factor over GF(q) of degree e > d/2.

Our long-term goal is to classify subgroups of G which contain fat elements. Following a result by Aschbacher this involves the classification of those subgroups H of G with fat elements which are quasi-simple, that is where H is a covering group of an alternating group, a quasi-simple group of Lie type, or a covering group of a sporadic simple group. In my talk I will mainly discuss the classification of subgroups with fat elements in the latter case of H being a covering group of a sporadic simple group.

All welcome.