Journal of Lie Theory, 7(2), 279-285 (1997)

On closed abelian subgroups of real Lie groups

M. Wüstner

Fachbereich Mathematik
Technische Hochschule Darmstadt
Schlossgartenstrasse 7
D-64289 Darmstadt
Abstract: Let $G$ be a locally compact real Lie group such that all abelian subgroups of $G/G_0$ are finite. Assume that $A\subseteq G$ is an closed abelian subgroup. Then $A$ is isomorphic to $\R^n\times\T^m\times\Z^k\times F$ where $F$ is a finite abelian group. If $C\subseteq G$ is a closed solvable subgroup, then $C$ is compactly generated.

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