# Algebraic automorphism

From Groupprops

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)

View other automorphism properties OR View other function properties

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.[SHOW MORE]

## Definition

### Symbol-free definition

An automorphism of a group is said to be **algebraic** if given any element of the group, the smallest subgroup containing that element which is invariant under the automorphism, is finitely generated.

### Definition with symbols

An automorphism of a group is said to be **algebraic** if for any the smallest subgroup for which , is finitely generated.