A note on hyperbolically embedded subgroups

Abstract

Let G be a group and H a subgroup of G. The notion of H being hyperbolically embedded in G was introduced by Dahmani, Guiraldel, and Osin. This note introduces an equivalent definition of hyperbolic embedded subgroup based on Bowditch’s approach to relatively hyperbolic groups in terms of fine graphs.

Keywords:

• Acylindrically hyperbolic
• fine graph
• hyperbolically embedded
• relatively hyperbolic

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20F65
• 20F67

Acknowledgments

We thank Hadi Bigdely for proof reading parts of the manuscript. We also thank the referee for comments and corrections. Some of the results of this note are based on the Master thesis of the second author at Memorial University of Newfoundland under the supervision of the first author [7]. In that work, an attempt to prove a weaker version of Theorem 1.2 is outlined, using a more restrictive notion of (G, H)-graph.

Additional information

Funding

Eduardo Martínez-Pedroza acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC).