Infinitely presented permutation stable groups and invariant random subgroups of metabelian groups
arxiv(2022)
摘要
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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关键词
stability, invariant random groups, wreath products, metabelian groups, amenable groups
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