Characteristic AEP-subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: characteristic subgroup and AEP-subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

A subgroup H of a group G is termed a characteristic AEP-subgroup if the homomorphism:

\operatorname{Aut}(G) \to \operatorname{Aut}(H)

that sends an automorphism of G to its restriction to H is well-defined (i.e., every automorphism of G does restrict to an automorphism of H) and surjective (i.e., every automorphism of H arises as the restriction of an automorphism of G).

Relation with other properties

Stronger properties

Weaker properties