Combination of quasiconvex subgroups of relatively hyperbolic groups

Abstract

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups $Q_1$ and $Q_2$ is quasiconvex and isomorphic to $Q_1{\ast }_{Q_1\cap Q_2}{Q}_2$. Our results generalize known combination theorems for quasiconvex subgroups of word hyperbolic groups. Some applications are presented.