A note on compact subgroups of topological groups

R. W. Bagley, M. R. Peyrovian

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Abstract

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.

Original languageEnglish
Pages (from-to)273-278
Number of pages6
JournalBulletin of the Australian Mathematical Society
Volume33
Issue number2
DOIs
StatePublished - Apr 1986

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