Groups, Geometry, and Dynamics


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Volume 3, Issue 2, 2009, pp. 317–342
DOI: 10.4171/GGD/59

Published online: 2009-06-30

Combination of quasiconvex subgroups of relatively hyperbolic groups

Eduardo Martínez Pedroza[1]

(1) Memorial University of Newfoundland, St. John's, Canada

For relatively hyperbolic groups, we investigate conditions guaranteeing that the subgroup generated by two quasiconvex subgroups Q1 and Q2 is quasiconvex and isomorphic to Q1Q1 ∩ Q1 Q2. Our results generalize known combination theorems for quasiconvex subgroups of word hyperbolic groups. Some applications are presented.

Keywords: Relatively hyperbolic group, quasi-convex subgroup, combination theorem, parabolic subgroup

Martínez Pedroza Eduardo: Combination of quasiconvex subgroups of relatively hyperbolic groups. Groups Geom. Dyn. 3 (2009), 317-342. doi: 10.4171/GGD/59