Acylindrical hyperbolicity of automorphism groups of infinitely ended groups

We prove that the automorphism group of every infinitely ended finitely generated is acylindrically hyperbolic. In particular Aut ( F n ) hyperbolic for ⩾ 2 . More generally, if G a which not virtually cyclic, and relative to finite collection P proper subgroups, then , As consequence, free-by-cyclic ⋊ φ Z only has infinite order in Out