Group in which every automorphism is class-preserving

Definition
A group is termed a group in which every automorphism is class-preserving if it satisfies the following equivalent conditions:


 * 1) Every defining ingredient::automorphism of the group is a defining ingredient::class-preserving automorphism, i.e., it sends each element to within its conjugacy class.
 * 2) Every element of the group is automorph-conjugate, i.e., if two elements of the group are related by an automorphism, then they are in fact conjugate elements, i.e., they are in the same conjugacy class.