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In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.

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How to compute the group cohomology of $\mathbb{Z}/n\mathbb{Z}\times \mathbb{Z}/n\mathbb{Z}$...

If $M$ is torsion-free (as a $\mathbb{Z}-$module), then the Kunneth formula still holds. If $M = \mathbb{Z}$ with trivial group action, then it holds by the corresponding result for the CW-complex cat …
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