This article defines a function property, viz a property of functions from a group to itself
Definition with symbols
A function is termed a monomial map if there exists a word and fixed elements such that for any :
Relation with other properties
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.