Uncountably many permutation stable groups

TL;DR

This paper proves that a large family of uncountably many 2-generated groups constructed by Neumann are permutation stable, using analysis of their invariant random subgroups.

Contribution

It demonstrates the permutation stability of Neumann's uncountably many 2-generated groups through invariant random subgroup analysis.

Findings

All of Neumann's constructed groups are permutation stable.

The structure of their invariant random subgroups underpins this stability.

The result extends understanding of stability properties in infinite groups.

Abstract

In a 1937 paper B.H. Neumann constructed an uncountable family of $2$-generated groups. We prove that all of his groups are permutation stable by analyzing the structure of their invariant random subgroups.