Ross, Kenneth A. Closed subgroups of compactly generated LCA groups are compactly generated. (English) Zbl 1414.22013 Topology Appl. 259, 378-383 (2019). 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. Cited in 2 Documents MSC: 22B05 General properties and structure of LCA groups Keywords:compactly generated locally compact groups; free group on two generators Citations:Zbl 0189.32504; Zbl 0222.22005 PDFBibTeX XMLCite \textit{K. A. Ross}, Topology Appl. 259, 378--383 (2019; Zbl 1414.22013) Full Text: DOI References: [1] Hall, Marshall, The Theory of Groups (1959), Macmillan Company: Macmillan Company New York · Zbl 0084.02202 [2] Hewitt, E.; Ross, K. A., Abstract Harmonic Analysis I (1979), Springer-Verlag [3] Hofmann, Karl H.; Neeb, Karl-Hermann, The compact generation of closed subgroups of locally compact groups, J. Group Theory, 12, 555-559 (2009) · Zbl 1179.22003 [4] Kurosh, A. G., The Theory of Groups, vol. 2 (1956), Chelsea Publishing Company: Chelsea Publishing Company New York [5] Lang, Serge, \(S L_2(R) (1975)\), Addison-Wesley · Zbl 0311.22001 [6] MacBeath, A. M.; Swierczkowski, On the set of generators of a subgroup, Nedl. Akad. Wet. Proc., Ser. A 62 = Indag. Math., 21, 280-281 (1959) · Zbl 0118.26503 [7] Morris, Sidney A., Locally compact abelian groups and the variety of topological groups generated by the reals, Proc. Am. Math. Soc.. Proc. Am. Math. Soc., Proc. Am. Math. Soc., 51, 290-292 (1975), (Erratum) · Zbl 0222.22005 [8] Morris, Sidney A., Pontryagin Duality and the Structure of Locally Compact Abelian Groups (1977), Cambridge University Press · Zbl 0446.22006 [9] Moskowitz, Martin, Homological algebra in locally compact abelian groups, Trans. Am. Math. Soc., 127, 361-404 (1967) · Zbl 0149.26302 [10] Saeki, Sadahiro, The \(L^p\)-conjecture and Young’s inequality, Ill. J. Math., 34, 614-627 (1990) · Zbl 0701.22003 [11] Specht, Wilhelm, Gruppentheorie (1956), Springer-Verlag: Springer-Verlag Berlin · Zbl 0074.25603 [12] Stroppel, Markus, Locally Compact Groups (2006), European Mathematical Society · Zbl 1102.22005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.