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Closed subgroups of compactly generated LCA groups are compactly generated. (English) Zbl 1414.22013

Summary: This is an update on the theorem stated in the title, where LCA abbreviates “locally compact abelian.” This was proved over 50 years ago by S. Grosser and M. Moskowitz [Trans. Am. Math. Soc. 129, 361–390 (1967; Zbl 0189.32504)] and independently by S. A. Morris [Proc. Am. Math. Soc. 34, 290–292 (1972; Zbl 0222.22005)]. The theorem does not generally hold if “abelian” is removed; in fact, it does not hold for the discrete free group on two generators. In this paper we give several results indicating when a closed subgroup of a compactly generated (not necessarily abelian) locally compact group is compactly generated.

MSC:

22B05 General properties and structure of LCA groups
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