Hyperbolically embedded virtually free subgroups of relatively hyperbolic groups

2011/09/13 by Matsuda, Yoshifumi, Oguni, Shin-ichi, Yamagata, Saeko
#20F65 #20F67 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1109.2663

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.

Related

• A non-quasiconvex embedding of relatively hyperbolic groups
• Finite Index Rigidity of Relatively Hyperbolic Groups
• A Note on Hyperbolically Embedded Subgroups
• A non-Hopfian relatively hyperbolic group with respect to a Hopfian subgroup
• Relative hyperbolicity of free extensions of free groups