# Intermediately AEP-subgroup

From Groupprops

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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]

## 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 of a group is termed an **intermediately AEP-subgroup** if for every subgroup of containing , is an AEP-subgroup of . In other words, every automorphism of extends to an automorphism of .

## 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

### Weaker properties

## 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 conditionABOUT INTERMEDIATE SUBROUP CONDITION:View all properties satisfying intermediate subgroup condition | View facts about intermediate subgroup condition