
Journal of Lie Theory 18 (2008), No. 2, 383390 Copyright Heldermann Verlag 2008 On the ProLie Group Theorem and the Closed Subgroup Theorem Karl H. Hofmann Fachbereich Mathematik, Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany hofmann@mathematik.tudarmstadt.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 [Abstractpdf] Let $H$ and $M$ be closed normal subgroups of a proLie 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: ProLie groups, closed subgroup theorem. MSC: 22A05 [ Fulltextpdf (164 KB)] for subscribers only. 