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.