Strong monomial 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 a strong monomial automorphism if it is a monomial automorphism and its inverse is a monomial automorphism.

Formalisms

Variety formalism

This automorphism property can be described in the language of universal algebra, viewing groups as a variety of algebras
View other such automorphism properties

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

Relation with other properties

Stronger properties

• Inner automorphism
• Strong power automorphism

Weaker properties

• Monomial automorphism
• Normal automorphism
• Weakly normal automorphism