The spectral sequence of a finite group extension stops

Abstract:

It is proved that if G is a finite group, H a normal subgroup, and A a finitely generated G-module, then both the cohomology and homology spectral sequences for the group extension stop in a finite number of stops. A lemma about ${\operatorname {Tor}}(M,N)$ as a module over $R \otimes S$ is proved. Two spectral sequences of Hochschild and Serre are shown to be the same.