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

• Characteristic direct factor
  • Normal Sylow subgroup
  • Normal Hall subgroup

Weaker properties

• Characteristic subgroup in which every subgroup characteristic in the whole group is characteristic
• Normal AEP-subgroup
• Characteristic subgroup
• AEP-subgroup