Virtual Amalgamation of Relatively Quasiconvex Subgroups

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.

7 pages, 1 figure

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