Compactly generated subgroups and open subgroups of locally compact groups

Authors:
R. W. Bagley, T. S. Wu and J. S. Yang

Journal:
Proc. Amer. Math. Soc. **103** (1988), 969-976

MSC:
Primary 22D05

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947692-0

MathSciNet review:
947692

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

**[1]**R. W. Bagley and T. S. Wu,*Maximal compact normal subgroups and pro-Lie groups*, Proc. Amer. Math. Soc.**93**(1985), 373-376. MR**770558 (86c:22005)****[2]**R. W. Bagley, T. S. Wu, and J. S. Yang,*On a class of topological group more general than*SIN*groups*, Pacific J. Math.**117**(1985), 209-217. MR**779917 (86k:22003)****[3]**-,*Pro-Lie groups*, Trans. Amer. Math. Soc.**287**(1985), 829-838. MR**768744 (86e:22006)****[4]**R. W. Bagley, and J. S. Yang,*Locally invariant toplogical groups and semidirect products*, Proc. Amer. Math. Soc.**93**(1985), 139-144. MR**766544 (86f:22004)****[5]**S. Grosser and M. Moskowitz,*Compactness conditions in topological groups*, J. Reine Angew Math.**246**(1971), 1-40. MR**0284541 (44:1766)****[6]**D. H. Lee,*Supplements for the identity component in locally compact groups*, Math. Z.**104**(1968), 28-49. MR**0223486 (36:6534)****[7]**D. Montgomery and L. Zippin,*Topological transformation groups*, Interscience, New York, 1965. MR**0073104 (17:383b)****[8]**V. P. Platonov,*The structure of topological locally projectively nilpotent groups and groups with a normalizer condition*, Mat. Sb. (N.S.)**114**(1967), 38-58. (Russian) MR**0202910 (34:2769)****[9]**M. S. Raghunathan,*Discrete subgroups of Lie groups*, Springer-Verlag, Berlin and New York, 1972. MR**0507234 (58:22394a)****[10]**J. Tits,*Free subgroups in linear groups*, J. Algebra**20**(1972), 250-270. MR**0286898 (44:4105)****[11]**S. P. Wang,*Compactness properties of topological groups*. III, Trans. Amer. Math. Soc.**209**(1975), 399-418. MR**0374329 (51:10529)****[12]**T. S. Wu,*On unimodular groups*, Bull. Inst. Math. Acad. Sinica**11**(1983), 485-491. MR**726995 (85h:22009)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0947692-0

Article copyright:
© Copyright 1988
American Mathematical Society