Algebraic automorphism

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 $$\sigma$$ of a group $$G$$ is said to be algebraic if for any $$g \in G$$ the smallest subgroup $$H \ni g$$ for which $$\sigma(H) = H$$, is finitely generated.

Relation with other properties

 * E-automorphism