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

Arie Levit, Alexander Lubotzky

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
JournalErgodic Theory and Dynamical Systems
DOIs
StateAccepted/In press - 2021
Externally publishedYes

Keywords

  • amenable groups
  • invariant random groups
  • metabelian groups
  • stability
  • wreath products

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