One-relator groups with torsion are conjugacy separable

TL;DR

This paper proves that one-relator groups with torsion are hereditarily conjugacy separable, extending to their quasiconvex subgroups, using recent advances in group theory.

Contribution

It establishes the conjugacy separability of one-relator groups with torsion and their quasiconvex subgroups, a significant advancement in understanding their algebraic structure.

Findings

One-relator groups with torsion are hereditarily conjugacy separable.

Quasiconvex subgroups of these groups are also conjugacy separable.

The proof combines recent results by Dani Wise and the first author.

Abstract

We prove that one-relator groups with torsion are hereditarily conjugacy separable. Our argument is based on a combination of recent results of Dani Wise and the first author. As a corollary we obtain that any quasiconvex subgroup of a one-relator group with torsion is also conjugacy separable.