Why do simply connected solvable analytic groups have no nontrivial compact subgroups? I'll appreciate any help on this question.
2026-03-27 03:49:06.1774583346
Why simply connected solvable analytic groups have no nontrivial compact subgroups?
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For a $n$-dimensional connected Lie group $G$ the maximal compact subgroup is trivial if and only if $G$ is diffeomorphic to $\mathbb{R}^n$. But if $G$ is simply connected and solvable, then it is diffeomorphic to $\mathbb{R}^n$. For references see here.