Volume 12, issue 4 (2012)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
Virtual amalgamation of relatively quasiconvex subgroups

Eduardo Martínez-Pedroza and Alessandro Sisto

Algebraic & Geometric Topology 12 (2012) 1993–2002
Abstract

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two relatively quasiconvex subgroups ${Q}_{1}$ and ${Q}_{2}$ is relatively quasiconvex and isomorphic to ${Q}_{1}{\ast }_{{Q}_{1}\cap {Q}_{2}}{Q}_{2}$. The main theorem extends results for quasiconvex subgroups of word-hyperbolic groups, and results for discrete subgroups of isometries of hyperbolic spaces. An application on separability of double cosets of quasiconvex subgroups is included.

Keywords
Relatively hyperbolic groups, quasiconvex subgroups, combination theorem, amalgamation, separability
Mathematical Subject Classification 2010
Primary: 20F65, 20F67