#### Volume 12, issue 4 (2012)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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