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irreducible lattices in locally compact groups

Ergodic Theory and Dynamical Systems (1)

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Simple groups and irreducible lattices in wreath products
Part of
- Structure and classification of infinite or finite groups
- Special aspects of infinite or finite groups
ADRIEN LE BOUDEC
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 5 / May 2021

Published online by Cambridge University Press:

07 February 2020, pp. 1502-1513

Print publication:

May 2021
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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.