Compactly generated subgroups and open subgroups of locally compact groups

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

doi:10.1090/S0002-9939-1988-0947692-0

Compactly generated subgroups and open subgroups of locally compact groups
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by R. W. Bagley, T. S. Wu and J. S. Yang PDF

Proc. Amer. Math. Soc. 103 (1988), 969-976 Request permission

Abstract:

This paper contains results of the following sort: If $G$ is a locally compact group and $H$ is a closed subgroup such that the coset space $G/H$ is locally connected, then $H{G_0}$ is open in $G$. If $G$ is a locally compact group such that $G/{G_0}$ is compact, then every closed subgroup of $G$ is compactly generated if and only if ${G_0}$ has no noncompact simple factor.

References

R. W. Bagley and T. S. Wu, Maximal compact normal subgroups and pro-Lie groups, Proc. Amer. Math. Soc. 93 (1985), no. 2, 373–376. MR 770558, DOI 10.1090/S0002-9939-1985-0770558-3
R. W. Bagley, T. S. Wu, and J. S. Yang, On a class of topological groups more general than SIN groups, Pacific J. Math. 117 (1985), no. 2, 209–217. MR 779917
R. W. Bagley, T. S. Wu, and J. S. Yang, Pro-Lie groups, Trans. Amer. Math. Soc. 287 (1985), no. 2, 829–838. MR 768744, DOI 10.1090/S0002-9947-1985-0768744-6
R. W. Bagley and J. S. Yang, Locally invariant topological groups and semidirect products, Proc. Amer. Math. Soc. 93 (1985), no. 1, 139–144. MR 766544, DOI 10.1090/S0002-9939-1985-0766544-X
Siegfried Grosser and Martin Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1–40. MR 284541, DOI 10.1515/crll.1971.246.1
Dong Hoon Lee, Supplements for the identity component in locally compact groups, Math. Z. 104 (1968), 28–49. MR 223486, DOI 10.1007/BF01114916
Deane Montgomery and Leo Zippin, Topological transformation groups, Interscience Publishers, New York-London, 1955. MR 0073104
V. P. Platonov, The structure of topological locally projectively nilpotent groups and groups with a normalizer condition, Mat. Sb. (N.S.) 72 (114) (1967), 38–58 (Russian). MR 0202910
M. S. Raghunathan, Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York-Heidelberg, 1972. MR 0507234
J. Tits, Free subgroups in linear groups, J. Algebra 20 (1972), 250–270. MR 286898, DOI 10.1016/0021-8693(72)90058-0
S. P. Wang, Compactness properties of topological groups. III, Trans. Amer. Math. Soc. 209 (1975), 399–418. MR 374329, DOI 10.1090/S0002-9947-1975-0374329-X
Ta Sun Wu, On unimodular groups, Bull. Inst. Math. Acad. Sinica 11 (1983), no. 3, 485–491. MR 726995