The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups

Details The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups

2011-06-27

arxiv.org/abs/1106.5288v2

Mathematics

Group Theory

27 pages; minor corrections

Scientific paper

We introduce a partial order on the set of relatively hyperbolic structures on a countable group and the universal relatively hyperbolic structure on the group for characterizing relatively hyperbolic structures on the group. A characterization of the universal relatively hyperbolic structure on a finitely generated group is given and it enables us to recognize several groups with the universal relatively hyperbolic structure. We also show that two relatively hyperbolic structures on a finitely generated group give the same set of relatively quasiconvex subgroups if and only if these structures are equal when we ignore virtually infinite cyclic subgroups.

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