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Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups
Published online by Cambridge University Press: 30 April 2021
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.
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- © The Author(s), 2021. Published by Cambridge University Press
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