Extended class-preserving automorphism

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This article defines an automorphism property, viz a property of group automorphisms. Hence, it also defines a function property (property of functions from a group to itself)
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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 conjugacy class or to an element in the conjugacy class of its inverse.

Relation with other properties

Stronger properties

• Inner automorphism
• Class-preserving automorphism
• Class-inverting automorphism

Weaker properties

• Normal automorphism
• Weakly normal automorphism