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Bagley, R. W.; Wu, T. S.; Yang, J. S.

Compact and compactly generated subgroups of locally compact groups. (English) Zbl 0696.22002

Proc. Am. Math. Soc. 108, No. 4, 1085-1094 (1990).
A locally compact topological group G is called an H(c)-group if every closed subgroup of G is compactly generated and the factor group G/K is a Lie group. G is called an H-group if G has a maximal compact normal subgroup with Lie factor. In this paper, conditions for a locally compact group G to be an H(c)-group and H-group are given. It is noticed that if G is an H(c)-group, then G itself must be a hereditary H-group. The authors also prove that if G has a compactly generated closed normal subgroup F such that both G/F and \(F/F_ 0\) are H-groups, then G is an H-group.
Reviewer: K.-P.Shum

MSC:

22A05 Structure of general topological groups
22D05 General properties and structure of locally compact groups

Keywords:

locally compact topological group; H(c)-group; closed subgroup; compactly generated; Lie group; H-group; maximal compact normal subgroup
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References:

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