# Strong monomial automorphism

## Contents

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