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Non-abelian group cohomology, additional information

Let $G$ be a (profinite) group, and let $M$ be a non-abelian $G$-module. We know how to construct reasonably $H^0(G,M)$ and $H^1(G,M)$ and it turns out that $H^1(G,M)$ is just a pointed set and not ...
Or Shahar's user avatar
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$G\cdot H$ with $G,H$ non-Abelian finite simple

Can a non-split extension of one non-Abelian finite simple group by another exist?
Daniel Sebald's user avatar