On the Involution Module of PSL(n,2^f)
Speaker: Lars Pforte (NUI Maynooth)
Date: Mon 28th January 2008
Location: Mathematical Sciences Seminar Room
For any finite group G the set I(G) of involutions in G is a G-set under conjugation. Let k be an algebraically closed field of characteristic 2. We refer to the resulting G-permutation module kI(G) as the permutation module of G. In this talk I will present some work on the involution module of the projective special linear group over a finite field of characteristic 2. Using inflation we will see that it is enough to focus on the involution module of the special linear group. I will introduce this module and using a theorem by M. Broue I want to determine the number of its components by examining which 2-groups are vertex of how many components. In small cases we will obtain a complete result.
(This talk is part of the Algebra/Claude Shannon Institute series.)