English

Infinitely presented stable groups and invariant random subgroups of metabelian groups

Group Theory 2019-11-27 v2 Dynamical Systems

Abstract

We prove that all invariant random subgroups of the lamplighter group LL are co-sofic. It follows that LL 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.

Keywords

Cite

@article{arxiv.1909.11842,
  title  = {Infinitely presented stable groups and invariant random subgroups of metabelian groups},
  author = {Arie Levit and Alexander Lubotzky},
  journal= {arXiv preprint arXiv:1909.11842},
  year   = {2019}
}

Comments

32 pages; small corrections