Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups

Abstract

We show that if a group is not virtually cyclic and is hyperbolic relative to a family of proper subgroups, then it has a hyperbolically embedded subgroup which contains a finitely generated non-abelian free group as a finite index subgroup.

13 pages, 1 figure, a remark on the main result is added

References in corpus (2)

• Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces
• Blowing up and down compacta with geometrically finite convergence actions of a group

Cited by in corpus (2)

• Blowing up and down compacta with geometrically finite convergence actions of a group
• A non-quasiconvex embedding of relatively hyperbolic groups