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Timeline for Group structure extension

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Jul 4, 2021 at 21:15 comment added Giulio @DenisT. can you say exactly which of cohomology group control this extension problem? Meaning specify the cotriple, the functors, and where one has to compute them. Thanks!
Jul 3, 2021 at 18:09 comment added Denis T In theory cotriple cohomology provides an answer for all extension problems of this sort; in practice, it's seldom computable.
Jul 2, 2021 at 16:42 comment added LSpice Presumably you mean group structures on $H$ such that there is a group embedding $i : G \to H$ over $G$ (or maybe I mean under …), together with some hypothesis on the resulting projection $H/i(G) \to X$ (maybe that the projection intertwines the action of $G$ on $H/i(G)$ by left translation with the given action of $G$ on $X$)?
Jul 2, 2021 at 16:29 history edited Giulio CC BY-SA 4.0
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Jul 2, 2021 at 15:53 history asked Giulio CC BY-SA 4.0