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Simple groups and irreducible lattices in wreath products

Part of: Special aspects of infinite or finite groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  07 February 2020

ADRIEN LE BOUDEC
ADRIEN LE BOUDEC*
Affiliation:
UCLouvain, IRMP, Chemin du Cyclotron 2, 1348Louvain-la-Neuve, Belgium CNRS, Unité de Mathématiques Pures et Appliquées, ENS-Lyon, France email adrien.le-boudec@ens-lyon.fr
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Abstract

We consider the finitely generated groups acting on a regular tree with almost prescribed local action. We show that these groups embed as cocompact irreducible lattices in some locally compact wreath products. This provides examples of finitely generated simple groups quasi-isometric to a wreath product $C\wr F$, where $C$ is a finite group and $F$ a non-abelian free group.

Keywords

groups acting on treesirreducible lattices in locally compact groupswreath products

MSC classification

Primary: 20E08: Groups acting on trees 20F65: Geometric group theory 20E32: Simple groups 20E22: Extensions, wreath products, and other compositions
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 5 , May 2021 , pp. 1502 - 1513
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Copyright
© The Author(s) 2020. Published by Cambridge University Press

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