# Questions tagged [group-cohomology]

a tool used to compute invariants of group actions using methods from homology theory, such as invariants, coinvariants, extensions... Use with (homology-cohomology).

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### Group cohomology reference

I'm interested in studying group cohomology (for discrete groups). Are there accessible (lecture) notes that give a nice overview of the basics for group cohomology and develop the categorical ...
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### Question on Group cohomology of $C_p \times C_p$

Let $G= C_p \times C_p$, where the cyclic group in the first factor is generated by $a$ and the second factor by $b.$ Let $H_j$ be a subgroup of $G$ generated by $(a, b^j)$ where $0 \le j \le p-1.$ ...
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### Free action of Group $G$ on $S^n$ gives free resolution of $\mathbb{Z}$ as a $\mathbb{Z}[G]$-module.

Suppose I have a group ${ G }$ acting freely on the sphere ${ S^n }$ for ${ n \geq 2 }$. Does this somehow get me a free resolution of ${ \mathbb{Z} }$ as a ${ \mathbb{Z}[G] }$-module? Forgive me if ...
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### What is the action on $H^1$ in Galois cohomology?

This is a question that I haven't been able to find answers for in the books I've looked at, so I wanted to ask it here to get some clarification. Given an abelian group $A$ and a Galois group $G$ ...
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### Bijection between isomorphism class of torsors and first cohomology set

Let $G$ be a profinite group and let $A$ be a $G$-group. A torsor over $A$ is a non-empty $G$-set $P$ endowed with a simply transitive right action $\star$ of $A$ which is compatible with the left ...
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