Acylindrical hyperbolicity of automorphism groups of infinitely ended groups

Abstract

We prove that the automorphism group of every infinitely ended finitely generated group is acylindrically hyperbolic. In particular (Formula presented.) is acylindrically hyperbolic for every (Formula presented.). More generally, if (Formula presented.) is a group which is not virtually cyclic, and hyperbolic relative to a finite collection (Formula presented.) of finitely generated proper subgroups, then (Formula presented.) is acylindrically hyperbolic. As a consequence, a free-by-cyclic group (Formula presented.) is acylindrically hyperbolic if and only if (Formula presented.) has infinite order in (Formula presented.).