Geodesic
On the Pro-Lie Group Theorem and the Closed Subgroup Theorem
Journal of Lie theory, Tome 18 (2008) no. 2, pp. 383-39

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22A05
Mots-clés : Pro-Lie groups, closed subgroup theorem 
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     author = {K. H. Hofmann and S. A. Morris },
     title = {On the {Pro-Lie} {Group} {Theorem} and the {Closed} {Subgroup} {Theorem}},
     journal = {Journal of Lie theory},
     pages = {383--39},
     publisher = {mathdoc},
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     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JLT_2008_18_2_JLT_2008_18_2_a8/}
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K. H. Hofmann; S. A. Morris . On the Pro-Lie Group Theorem and the Closed Subgroup Theorem. Journal of Lie theory, Tome 18 (2008) no. 2, pp. 383-39. http://geodesic.mathdoc.fr/item/JLT_2008_18_2_JLT_2008_18_2_a8/