Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Lie Theory 18 (2008), No. 2, 383--390Copyright Heldermann Verlag 2008 On the Pro-Lie Group Theorem and the Closed Subgroup Theorem Karl H. Hofmann Fachbereich Mathematik, Technische Universität, 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 [ Fulltext-pdf  (164  KB)] for subscribers only.