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Questions about the branch of algebra that deals with groups.

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Cohomologically trivial module $M$ such that $M/pM$ is not cohomologically trivial for some ...

I was reading Brown's Cohomology Theory of Finite groups and was wondering whether there's an example of the following. Let $n\in \mathbb{N}$. Does there exist a $\mathbb{Z}_n$ module $M$ which is co …
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