A Note on Quasiconvexity and Relative Hyperbolic Structures
نویسندگان
چکیده
Let G be a group which is hyperbolic relative to a collection of subgroups H1, and it is also hyperbolic relative to a collection of subgroups H2. Suppose that H2 ⊂ H1. We characterize, for subgroups of G, when quasiconvexity relative to H1 implies quasiconvexity relative to H2. We also show that quasiconvexity relative toH2 implies quasiconvexity relative toH1. As an application, we give some extensions of combination theorems for quasiconvex subgroups of relatively hyperbolic groups.
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