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BOUNDED CONJUGACY CLASSES AND CONJUGACY CLASSES SUPPORTING INVARIANT MEASURES AND AUTOMORPHISMS

Part of: Probability theory on algebraic and topological structures Locally compact groups and their algebras

Published online by Cambridge University Press:  06 February 2025

C. R. E. RAJA Open the ORCID record for C. R. E. RAJA [Opens in a new window]
C. R. E. RAJA*
Affiliation:
Stat-Math Unit, Indian Statistical Institute (ISI), 8th Mile Mysore Road, Bangalore 560 059, India
*
e-mail: [email protected]
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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.

Keywords

locally compact groupconjugacy classfinite measuresautomorphismtdlc group

MSC classification

Primary: 22D05: General properties and structure of locally compact groups
Secondary: 22D45: Automorphism groups of locally compact groups 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 6
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The work was supported by SERC grant under MATRICS MTR/2022/000429.

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