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Dec 14, 2023 at 21:25 comment added David White +1 Thanks for writing all this up. It's good to have clear proofs spelled out, and not that easy to find in the literature. So, now the OP has a counterexample in the non-Lie case, and a proof in the case of compact Lie groups.
Dec 14, 2023 at 17:50 history answered Tyrone CC BY-SA 4.0