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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


Author: M. R. Peyrovian
Journal: Proc. Amer. Math. Soc. 99 (1987), 389-394
MSC: Primary 22D05
MathSciNet review: 870807
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Abstract: The main concern is the existence of a maximal compact normal subgroup $ K$ in a locally compact group $ G$, and whether or not $ G/K$ is a Lie group. $ G$ has a maximal compact subgroup if and only if $ G/{G_0}$ has. Maximal compact subgroups of totally disconnected groups are open. If the bounded part of $ G$ is compactly generated, then $ G$ has a maximal compact normal subgroup $ K$ and if $ B(G)$ is open, then $ G/K$ is Lie. Generalized FC-groups, compactly generated type I IN-groups, and Moore groups share the same properties.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0870807-9
PII: S 0002-9939(1987)0870807-9
Article copyright: © Copyright 1987 American Mathematical Society