2016/02/10 by Oleg Bogopolski, Bogopolski, Oleg, Kai-Uwe Bux +2
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR
paper · pdf · doi:10.48550/arxiv.1602.03229
22 pages, 4 figures. Introduction is rewritten
openalex publication_date 2016/02/10 · arxiv created 2016/02/19 · arxiv updated 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 closed hyperbolic 3-manifolds and torsion-free small cancellation groups with finite C'(1/6) or C'(1/4)-T(4) presentations are hereditarily quasiconvex-SCS and hereditarily quasiconvex-SICS, and that surface groups are SCS and SICS. We also show that the word "quasiconvex" cannot be deleted for at least small cancellation groups.