# Monomial map

*This article defines a function property, viz a property of functions from a group to itself*

## Contents

## Definition

### Definition with symbols

A function is termed a **monomial map** if there exists a word and fixed elements such that for any :

A monomial map which defines an endomorphism is termed a monomial endomorphism. A monomial map which defines an automorphism is termed a monomial automorphism.

## Relation with other properties

### Inner automorphisms

An inner automorphism is a map of the form where is a *fixed* element. It thus fits into the definition of a monomial map. In fact, inner automorphisms are monomial automorphisms.

### Universal power maps

A universal power map is a map of the form where is a fixed integer. clearly a universal power map is a monomial map, in fact, it is a monomial map with no parameters.

In particular universal power automorphisms are monomial automorphisms and universal power endomorphisms are monomial endomorphisms.