BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS

Abstract We consider conjugacy classes in a locally compact group G that support finite G -invariant measures. If G is a property (M) extension of an abelian group, in particular, if G is a metabelian group, then any such conjugacy class is relatively compact. As an application, centralisers of lattices in such groups have bounded conjugacy classes. We use the same techniques to obtain results in the case of totally disconnected, locally compact groups.

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Publication Details

Journal
Bulletin of the Australian Mathematical Society
Published
2025-02-06
DOI
https://doi.org/10.1017/s0004972724001266
Primary Topic
Advanced Topology and Set Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS

C. R. E. Raja
Bulletin of the Australian Mathematical Society
Advanced Topology and Set Theory
article

BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS

C. R. E. Raja
article en

Abstract

Abstract We consider conjugacy classes in a locally compact group G that support finite G -invariant measures. If G is a property (M) extension of an abelian group, in particular, if G is a metabelian group, then any such conjugacy class is relatively compact. As an application, centralisers of lattices in such groups have bounded conjugacy classes. We use the same techniques to obtain results in the case of totally disconnected, locally compact groups.

Bulletin of the Australian Mathematical SocietyVol. 112(3)
Indian Statistical Institute (IN)
Openalex Percentile: Top 95%
Advanced Topology and Set Theory
DOIOpen Access PDFOpenAlex
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BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS — C. R. E. Raja · Bulletin of the Australian Mathematical Society (2025) | TGRS Research Map | TGRS