Intense Automorphisms of Finite Groups

Let G be a group. An automorphism of G is called intense if it sends each subgroup of G to a conjugate; the collection of such automorphisms is denoted by Int(G). In the special case in which p is a prime number and G is a finite p-group, one can show that Int(G) is the semidirect product of a normal p-Sylow and a cyclic subgroup of order dividing p-1. In this paper we classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges from our investiga…