For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1 ∗Q1 ∩ Q1 Q2. Our results generalize known combination theorems for quasiconvex subgroups of word hyperbolic groups. Some applications are presented.
Cite this article
Eduardo Martínez-Pedroza, Combination of quasiconvex subgroups of relatively hyperbolic groups. Groups Geom. Dyn. 3 (2009), no. 2, pp. 317–342DOI 10.4171/GGD/59