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The Union of Compact Subgroups of an Analytic Group
Let $G$ be an analytic group. Let $\Omega (G)$ be the union of all compact subgroups of $G$. We give a necessary and sufficient condition for $\Omega (G)$ to be dense in $G$ in terms of the action of a maximal compact torus $T$ of $G$ on the nilradical $N$ …