Journal of Lie Theory

no. 2
On the Pro-Lie Group Theorem and the Closed Subgroup Theorem
Journal of Lie Theory, Volume 18 (2008) no. 2, pp. 383-390
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.
DOI: 10.5802/jolt.501
Classification: 22A05
Keywords: Pro-Lie groups, closed subgroup theorem 
@article{JOLT_2008_18_2_a8,
     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--390},
     year = {2008},
     volume = {18},
     number = {2},
     doi = {10.5802/jolt.501},
     zbl = {1148.22002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.501/}
}
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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, Volume 18 (2008) no. 2, pp. 383-390. doi: 10.5802/jolt.501

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