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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.

5 votes
2 answers
1k views

symmetric 2-cocycle / many projective representations

Let $G$ be a finite group, $k$ the field of complex numbers. Are there (cohomologically nontrivial) group 2-cocycles $\sigma\in Z^2(G,k^\times)$ such that for all $g,h\in G$: $$\sigma(g,h)=\si …
5 votes

Inseparable Galois Cohomology

I cannot answer your question, but point to the right algebraic framework in my opinion: There is a well worked out classical (but somewhat underestimated) theory of inseparable Galois extensions. It …
Simon Lentner's user avatar