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Proceedings of the American Mathematical Society
Journal Article

Maximal Compact Normal Subgroups

M. R. Peyrovian
Proceedings of the American Mathematical Society
Vol. 99, No. 2 (Feb., 1987), pp. 389-394
Published by: American Mathematical Society
DOI: 10.2307/2046647
https://www.jstor.org/stable/2046647
Page Count: 6

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Topics: Lie groups, Topological compactness, Existence theorems, Topological theorems
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Maximal Compact Normal Subgroups
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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/G0 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.
Proceedings of the American Mathematical Society © 1987 American Mathematical Society