Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

Arie Levit; Alexander Lubotzky

doi:10.1017/etds.2021.9

Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

Arie Levit, Alexander Lubotzky

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove that all invariant random subgroups of the lamplighter group L are co-sofic. It follows that L is permutation stable, providing an example of an infinitely presented such group. Our proof applies more generally to all permutational wreath products of finitely generated abelian groups. We rely on the pointwise ergodic theorem for amenable groups.

Original language	English
Pages (from-to)	2028-2063
Number of pages	36
Journal	Ergodic Theory and Dynamical Systems
Volume	42
Issue number	6
DOIs	https://doi.org/10.1017/etds.2021.9
State	Published - 30 Jun 2022

Bibliographical note

Publisher Copyright:
©

Keywords

amenable groups
invariant random groups
metabelian groups
stability
wreath products

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10.1017/etds.2021.9

Cite this

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KW - wreath products

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Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups

Abstract

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Keywords

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