One-relator groups with torsion are conjugacy separable. (Q2437437)

A group \(G\) is conjugacy separable if for any two non-conjugate elements \(x,y\in G\) there is a homomorphism from \(G\) to a finite group \(M\) such that the images of \(x\) and \(y\) are not conjugate in \(M\). The group \(G\) is hereditarily conjugacy separable if every finite index subgroup of \(G\) is conjugacy separable. The authors prove that one-relator groups with torsion are hereditarily conjugacy separable. As a corollary they obtain that any quasiconvex subgroup of a one-relator group with torsion is also conjugacy separable.