The Spectral Sequence of a Finite Group Extension Stops

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 <!-- MATH ${\operatorname{Tor}}(M,N)$ --> as a module over <!-- MATH $R \otimes S$ --> is proved. Two spectral sequences of Hochschild and Serre are shown to be the same.