Virtually free groups are stable in permutations

TL;DR

This paper proves that finitely generated virtually free groups exhibit stability in permutations, and applies this to show that almost-automorphisms of labelled graphs are near true automorphisms.

Contribution

It establishes the stability of finitely generated virtually free groups in permutations and connects this to automorphism approximations in labelled graphs.

Findings

Virtually free groups are stable in permutations.

Almost-automorphisms of labelled graphs are close to automorphisms.

Provides a new link between group stability and graph automorphisms.

Abstract

We prove that finitely generated virtually free groups are stable in permutations. As an application, we show that almost-periodic almost-automorphisms of labelled graphs are close to periodic automorphisms.