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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Contents

This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term
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View other semistandard definitions in group theory
This is a variation of inner automorphism
View a complete list of variations of inner automorphism OR read a survey article on varying inner automorphism

Definition

A monomial automorphism is a monomial map that is also an automorphism

Further information: monomial map

Definition with symbols

An automorphism f:G \to G is termed a monomial automorphism if there exists a word w(x,y_1,y_2,\ldots,y_n) and fixed elements a_1,a_2,\ldots,a_n \in G such that for any g \in G:

f(g) = w(g,a_1,a_2,\ldots,a_n)

If we remove the condition of f being an automorphism, we get the more general notion of a monomial map.

Relation with other properties

Stronger properties

Weaker properties

Metaproperties

Template:Monoid-closed ap

A product of monomial automorphisms is a monomial automorphism. This follows from the following two facts:

  • A product of automorphisms is an automorphism
  • A product of monomial maps is a monomial map
Facts about Monomial automorphismRDF feed
Stronger thanMonomially generated automorphism  +, Intrinsically continuous automorphism  +, and Normal automorphism  +
Weaker thanInner automorphism  +, Universal power automorphism  +, and Strongly monomial automorphism  +
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