Strong monomial automorphism

Definition
An automorphism $$\sigma$$ of a group $$G$$ is termed a strong monomial automorphism if it is a defining ingredient::monomial automorphism and its inverse is a monomial automorphism.

Formalisms
A strong monomial automorphism is a strong formula automorphism in the variety of groups, viewed as a variety of algebras.

Stronger properties

 * Weaker than::Inner automorphism
 * Weaker than::Strong power automorphism

Weaker properties

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