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A note on compact subgroups of topological groups

Published online by Cambridge University Press:  17 April 2009

R. W. Bagley  and
M. R. Peyrovian
R. W. Bagley
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, Florida
M. R. Peyrovian
Affiliation:
Department of Mathematics, University of Miami, Coral Gables, Florida
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Abstract

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Our main concern is the existence of maximal compact subgroups in a locally compact topological group. If G is a locally compact group such that P(G/G o), the set of periodic points of G/Go, is a compact subgroup of G/Go, than G has maximal compact subgroups K such that G/N is a Lie group where N = ∩K, the intersection of the collection K of all maximal compact subgroups of G. Also every compact subgroup of G is contained in a maximal compact subgroup. We given an example of a discrete group which has maximal finite subgroup and has finite subgroups not contained in maximal finite subgroups. We note that the above result on P(G/Go) is an extension of the well-known corresponding result for almost connected groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 2 , April 1986 , pp. 273 - 278
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Bagley, R. w., Wu, T. S. and Yang, J. S., “Locally compact groups in general settings”, (submitted).Google Scholar
[2]Hochschild, G., The Structure of Lie groups, (San Francisco 1965).Google Scholar
[3]Montgomery, D. and Zippin, L., Topological transformation groups, (Interscience, New York, London 1955.)Google Scholar
[4]Mostow, G. D., “Self-adjoiunt groups”, Ann. of Math. 62 (1955), 44–55.CrossRefGoogle Scholar
[5]Peyrovian, M. R., “Maximal compact normal subgroups”, Proc. Amer. Math. Soc. (to appear).Google Scholar