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Locally compact groups: maximal compact subgroups and N-groups

Published online by Cambridge University Press:  24 October 2008

R. W. Bagley ,
T. S. Wu  and
J. S. Yang
R. W. Bagley
Affiliation:
Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124, U.S.A.
T. S. Wu
Affiliation:
Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, OH 44106, U.S.A.
J. S. Yang
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.
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Abstract

If G is a locally compact group such that G/G0 contains a uniform compactly generated nilpotent subgroup, then G has a maximal compact normal subgroup K such that G/G is a Lie group. A topological group G is an N-group if, for each neighbourhood U of the identity and each compact set C ⊂G, there is a neighbourhood V of the identity such that for each g∈G. Several results on N-groups are obtained and it is shown that a related weaker condition is equivalent to local finiteness for certain totally disconnected groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 1 , July 1988 , pp. 47 - 64
Copyright
Copyright © Cambridge Philosophical Society 1988

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