Anja Meyer

Finite matrix groups; cohomology and stable elements

In their 1956 book Cartan and Eilenberg show results that tell us that the modular cohomology of a finite group G is equal to the set of stable elements in the modular cohomology of a Sylow p-subgroup of G. In this talk we will look at the groups SL_2(Z/p^n) for n>1. Their cohomology is not yet known, however there is a way to obtain the cohomology, using a combination of tools from homological algebra, profinite group theory, and fusion systems. We will introduce the concepts used and show how they can facilitate the explicit computations.