摘要
A group G is acylindrically hyperbolic if it admits a non-elementary acylindrical action on a hyperbolic space. We prove that every acylindrically hyperbolic group G has a generating set X such that the corresponding Cayley graph Gamma is a (non-elementary) quasi-tree and the action of G on Gamma is acylindrical. Our proof utilizes the notions of hyperbolically embedded subgroups and projection complexes. As an application, we obtain some new results about hyperbolically embedded subgroups and quasi-convex subgroups of acylindrically hyperbolic groups.
- 出版日期2017