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Journal of Lie Theory 18 (2008), No. 2, 383--390
Copyright Heldermann Verlag 2008



On the Pro-Lie Group Theorem and the Closed Subgroup Theorem

Karl H. Hofmann
Fachbereich Mathematik, Technische Universitšt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
hofmann@mathematik.tu-darmstadt.de

Sidney A. Morris
School of Information Technology and Mathematical Sciences, University of Ballarat, P. O. Box 663, Ballarat, Vic. 3353, Australia
s.morris@ballarat.edu.au



[Abstract-pdf]

Let $H$ and $M$ be closed normal subgroups of a pro-Lie group $G$ and assume that $H$ is connected and that $G/M$ is a Lie group. Then there is a closed normal subgroup $N$ of $G$ such that $N\subseteq M$, that $G/N$ is a Lie group, and that $HN$ is closed in $G$. As a consequence, $H/(H\cap N)\to HN/N$ is an isomorphism of Lie groups.

Keywords: Pro-Lie groups, closed subgroup theorem.

MSC: 22A05

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