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Questions about the branch of algebra that deals with groups.
2
votes
Lie groups admitting flat (bi)invariant metrics.
I'm a few years late with my answer, but if you're interested in the pseudo-Riemannian case as well, there is a structure theorem due to Baues for Lie algebras with invariant scalar products, see Theo …
2
votes
Uniform lattice in semidirect product
I'm a bit late to the party, but just want to remark that the reference given by YCor (Corollary 8.28 in Raghunathan) is actually known to be incorrect.
Counterexamples are known, first due to Starkov …