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invariant random groups

Ergodic Theory and Dynamical Systems (1)

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Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups
Part of
- Special aspects of infinite or finite groups
- Ergodic theory
ARIE LEVIT, ALEXANDER LUBOTZKY
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 6 / June 2022

Published online by Cambridge University Press:

30 April 2021, pp. 2028-2063

Print publication:

June 2022
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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.