# Formula automorphism

From Groupprops

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This article defines a property that can be evaluated for an automorphism of an algebra in a variety of algebras. The evaluation of that property depends on the ambient variety, and not just on the automorphism or the algebra.

View all such properties

## Definition

Let be a variety of algebras and be an algebra in . A **formula automorphism** is an automorphism of given by:

where is a word (or expression) in the s, using the operations of , and the are elements of .

A strong formula automorphism is a formula automorphism whose inverse is also a formula automorphism.

## Particular cases

### For groups

In the case of groups, the formula automorphisms are called monomial automorphisms. An automorphism such that both that and its inverse are monomial is termed a strong monomial automorphism.