Limit Groups are Subgroup Conjugacy Separable

Abstract

A group $G$ is called subgroup conjugacy separable if for every pair of non-conjugate finitely generated subgroups of $G$, there exists a finite quotient of $G$ where the images of these subgroups are not conjugate. We prove that limit groups are subgroup conjugacy separable. We also prove this property for one relator groups of the form $R=⟨a_1,...,a_n\mid W^n⟩$ with $n>|W|$. The property is also proved for virtual retracts (equivalently for quasiconvex subgroups) of hyperbolic virtually special groups.

References in corpus (3)

• On conjugacy separability of graph products of groups
• Subgroup conjugacy separability for surface groups
• On subgroup conjugacy separability in the class of virtually free groups