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Aug 2, 2020 at 18:10 comment added Denis Nardin I think the general approach is sound, but all you need for the morphism to lift is that the extension is split (which doesn't mean it's trivial, since semidirect products exist), so you'll need done kind of pointed set of "extensions modulo splittings"
Aug 2, 2020 at 17:53 history edited Josh Lackman CC BY-SA 4.0
added 118 characters in body
Aug 2, 2020 at 17:46 history answered Josh Lackman CC BY-SA 4.0