Integral Group Cohomology

Abstract

In this thesis we look closer at properties of integral group cohomology. In particular, we introduce the Lyndon-Hochschild-Serre spectral sequence which has a useful product structure which we use to prove that the group cohomology ring $\HH^{\star}(G,\Z)$ for a finite group $G$ is Noetherian. The proof was given by Leonard Evens in 1961. We also give a recursive algorithm for computing all cohomology groups of finite abelian groups.