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LOCALLY COMPACT WREATH PRODUCTS

Part of: Locally compact groups and their algebras Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  15 August 2018

YVES CORNULIER
YVES CORNULIER*
Affiliation:
CNRS and Univ Lyon, Univ Claude Bernard Lyon 1, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne, France email cornulier@math.univ-lyon1.fr
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Abstract

Wreath products of nondiscrete locally compact groups are usually not locally compact groups, nor even topological groups. As a substitute introduce a natural extension of the wreath product construction to the setting of locally compact groups. Applying this construction, we disprove a conjecture of Trofimov, constructing compactly generated locally compact groups of intermediate growth without any open compact normal subgroup.

Keywords

Locally compact groupswreath product

MSC classification

Primary: 20E22: Extensions, wreath products, and other compositions
Secondary: 20F69: Asymptotic properties of groups 22D05: General properties and structure of locally compact groups 22D10: Unitary representations of locally compact groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 107 , Issue 1 , August 2019 , pp. 26 - 52
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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Footnotes

The author was supported by ANR 12-BS01-0003-01 GDSous.

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