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)
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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 σ of a group G is said to be algebraic if for any 
the smallest subgroup 
for which σ(H) = H, is finitely generated.
