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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.

27 votes

Why does non-abelian group cohomology exist?

To elaborate on Eric's answer, I believe that $H^{1-n}(G, A)$ is $\pi_n$ of the homotopy fixed point space $K(A, 1)^{hG}$. That exact sequence which ends at $H^1$ - which is only a set, while $H^0$ i …
Reid Barton's user avatar
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