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Infinitely presented stable groups and invariant random subgroups of metabelian groups

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 نشر من قبل Arie Levit
 تاريخ النشر 2019
  مجال البحث
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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 a 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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