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Questions about the branch of algebra that deals with groups.

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Some sort of twisted group homomorphism

Start with a group $G$ that acts on a set $X$, and a second group $H$. We want to consider functions $\varphi: G \times X \to H$ such that $\varphi(g g', x) = \varphi(g, g'x) \varphi(g', x)$ for all $ …
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