Maximal compact normal subgroups

Peyrovian, M. R.

doi:10.1090/S0002-9939-1987-0870807-9

Maximal compact normal subgroups
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by M. R. Peyrovian

Proc. Amer. Math. Soc. 99 (1987), 389-394

DOI: https://doi.org/10.1090/S0002-9939-1987-0870807-9

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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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