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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Maximal compact normal subgroups and pro-Lie groups


Authors: R. W. Bagley and T. S. Wu
Journal: Proc. Amer. Math. Soc. 93 (1985), 373-376
MSC: Primary 22D05
MathSciNet review: 770558
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Abstract: We are concerned with conditions under which a locally compact group $ G$ has a maximal compact normal subgroup $ K$ and whether or not $ G/K$ is a Lie group. If $ G$ has small compact normal subgroups $ K$ such that $ G/K$ is a Lie group, then $ G$ is pro-Lie. If in $ G$ there is a collection of closed normal subgroups $ \{ {H_\alpha }\} $ such that $ \cap {H_\alpha } = e$ and $ G/{H_\alpha }$ is a Lie group for each $ \alpha $, then $ G$ is a residual Lie group. We determine conditions under which a residual Lie group is pro-Lie and give an example of a residual Lie group which is not embeddable in a pro-Lie group.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0770558-3
PII: S 0002-9939(1985)0770558-3
Article copyright: © Copyright 1985 American Mathematical Society