Intermediately AEP-subgroup

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

Symbol-free definition

A subgroup of a group is termed an intermediately AEP-subgroup if it is an AEP-subgroup in every intermediate subgroup.

Definition with symbols

A subgroup $H$ of a group $G$ is termed an intermediately AEP-subgroup if for every subgroup $K$ of $G$ containing $H$, $H$ is an AEP-subgroup of $K$. In other words, every automorphism of $H$ extends to an automorphism of $K$.

Formalisms

In terms of the intermediately operator

This property is obtained by applying the intermediately operator to the property: AEP-subgroup
View other properties obtained by applying the intermediately operator

Relation with other properties

Stronger properties

• Direct factor
• Normal intermediately AEP-subgroup

Weaker properties

• AEP-subgroup

Metaproperties

Intermediate subgroup condition

YES: This subgroup property satisfies the intermediate subgroup condition: if a subgroup has the property in the whole group, it has the property in every intermediate subgroup.
ABOUT THIS PROPERTY: View variations of this property satisfying intermediate subgroup condition | View variations of this property not satisfying intermediate subgroup condition
ABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition