2016
DOI: 10.48550/arxiv.1602.03229
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On subgroup conjugacy separability of hyperbolic QVH-groups

Oleg Bogopolski,
Kai-Uwe Bux

Abstract: A group G is called subgroup conjugacy separable (abbreviated as SCS) if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. An into-conjugacy version of SCS is abbreviated by SICS. We prove that if G is a hyperbolic group, H1 is a quasiconvex subgroup of G, and H2 is a subgroup of G which is elementwise conjugate into H1, then there exists a finite index subgroup of H2 which is conjugate into H1. As corollary, we deduce that fundamental groups of clos… Show more

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“…The objective of this paper is to show that the fundamental group of a hyperbolic 3-manifold is subgroup conjugacy separable. Bogopolski and Bux posed it as an open question on page 3 in [6].…”
Section: Introductionmentioning
confidence: 99%
“…The objective of this paper is to show that the fundamental group of a hyperbolic 3-manifold is subgroup conjugacy separable. Bogopolski and Bux posed it as an open question on page 3 in [6].…”
Section: Introductionmentioning
confidence: 99%