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.