Algebraic automorphism

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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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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 \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