Combination of quasiconvex subgroups of relatively hyperbolic groups
Combination of quasiconvex subgroups of relatively hyperbolic groups
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 ∗_{Q_1 ∩ Q_2} Q_2 . Our results generalize known combination theorems for quasiconvex subgroups of word hyperbolic groups. Some applications are presented.