Extended class-preserving automorphism

Definition
An automorphism $$\sigma$$ of a group $$G$$ is termed an extended class-preserving automorphism if it sends every element either to an element in its defining ingredient::conjugacy class or to an element in the conjugacy class of its inverse.

Stronger properties

 * Weaker than::Inner automorphism
 * Weaker than::Class-preserving automorphism
 * Weaker than::Class-inverting automorphism

Weaker properties

 * Stronger than::Normal automorphism
 * Stronger than::Weakly normal automorphism