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 are co-sofic. It follows that 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