High Quality Content by WIKIPEDIA articles! In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper, group cohomology is a way to study groups using a sequence of functors Hn. The study of fixed points of groups acting on modules and quotient modules is a motivation, but the cohomology can be defined using various constructions. There is a dual theory, group homology, and a generalization to non-abelian coefficients.