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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Pro-Lie groups

Authors: R. W. Bagley, T. S. Wu and J. S. Yang
Journal: Trans. Amer. Math. Soc. 287 (1985), 829-838
MSC: Primary 22D05
MathSciNet review: 768744
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Abstract: A topological group $ G$ is pro-Lie if $ G$ has small compact normal subgroups $ K$ such that $ G/K$ is a Lie group. A locally compact group $ G$ is an $ L$-group if, for every neighborhood $ U$ of the identity and compact set $ C$, there is a neighborhood $ V$ of the identity such that $ gH{g^{ - 1}} \cap C \subset U$ for every $ g \in G$ and every subgroup $ H \subset V$. We obtain characterizations of pro-Lie groups and make several applications. For example, every compactly generated $ L$-group is pro-Lie and a compactly generated group which can be embedded (by a continuous isomorphism) in a pro-Lie group is pro-Lie. We obtain related results for factor groups, nilpotent groups, maximal compact normal subgroups, and generalize a theorem of Hofmann, Liukkonen, and Mislove [4].

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Article copyright: © Copyright 1985 American Mathematical Society

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