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Relative quasiconvexity using fine hyperbolic graphs. (English) Zbl 1229.20038
The authors give a new definition of relatively quasiconvex subgroups of a relatively hyperbolic group. The definition is in the context of Bowditch’s approach to relative hyperbolicity using cocompact actions on fine hyperbolic graphs. The notion applies for all countable and a class of uncountable relatively hyperbolic groups. The authors show that it is equivalent to the definitions studied by Hruska for countable relatively hyperbolic groups. The authors also provide an elementary and self-contained proof that relatively quasiconvex subgroups are relatively hyperbolic.

MSC:
20F67 Hyperbolic groups and nonpositively curved groups
20F65 Geometric group theory
20E07 Subgroup theorems; subgroup growth
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F06 Cancellation theory of groups; application of van Kampen diagrams
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References:
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