Finite complete group

Definition
A finite complete group is a finite group that is also a defining ingredient::complete group: it satisfies the following two conditions:


 * It is a defining ingredient::centerless group: its center is trivial.
 * It is a defining ingredient::group in which every automorphism is inner.

In other words, a finite complete group is a finite group $$G$$ such that the natural map $$G \to \operatorname{Aut}(G)$$ is an isomorphism.

Stronger properties

 * Weaker than::Automorphism group of finite simple non-abelian group
 * Weaker than::Automorphism group of finite characteristically simply non-abelian group:
 * Weaker than::Finite complete solvable group