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Journal of Lie Theory, 7(2), 279-285 (1997)
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On closed abelian subgroups of real Lie groups

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M. Wüstner

Fachbereich Mathematik

Technische Hochschule Darmstadt

Schlossgartenstrasse 7

D-64289 Darmstadt

wuestner@mathematik.th-darmstadt.de

**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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