Hyperbolic 3-manifold groups are subgroup into conjugacy separable

Abstract

A group G is subgroup conjugacy distinguished (resp. subgroup into conjugacy separable) if whenever an element y (resp. a finitely generated subgroup K) is not conjugate to an element (to a subgroup) of a finitely generated subgroup H of G there exists a finite quotient G/N of G where yN (resp. KN/N) is not conjugate to an element (to a subgroup) of HN/N. We prove that the fundamental group of a hyperbolic 3-manifold is subgroup conjugacy distinguished and subgroup into conjugacy separable.

Keywords:

• Hyperbolic manifolds
• profinite topology
• hyperbolic groups
• finitely generated subgroups
• fundamental groups

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20E26
• 20E18
• 20F67

Additional information

Funding

The first author was supported by FAPDF and the second author was supported by FAPDF and CNPq.