A hyperbolic free-by-cyclic group determined by its finite quotients

TL;DR

This paper demonstrates that a specific hyperbolic free-by-cyclic group is uniquely determined by its finite quotients, establishing a new example of profinite rigidity in this class.

Contribution

It provides the first example of a hyperbolic free-by-cyclic group that is profinitely rigid among such groups.

Findings

The group is profinitely rigid among free-by-cyclic groups.

This is the first known hyperbolic free-by-cyclic group with this property.

The result advances understanding of group rigidity and finite quotients.

Abstract

We show that the group $\langle a,b,c,t : a^t=b,b^t=c,c^t=ca^{-1} \rangle$ is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-cyclic group with this property.