Intersection of automorph-conjugate subgroups

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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

A subgroup of a group is termed an intersection of automorph-conjugate subgroups if it can be expressed as the intersection of (possibly infinitely many) automorph-conjugate subgroups.

Formalisms

In terms of the intersection-closure operator

This property is obtained by applying the intersection-closure operator to the property: automorph-conjugate subgroup
View other properties obtained by applying the intersection-closure operator

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Characteristic subgroup	invariant under all automorphisms			|FULL LIST, MORE INFO
Automorph-conjugate subgroup	all automorphic subgroups are conjugate			|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Core-characteristic subgroup	its normal core is a characteristic subgroup			|FULL LIST, MORE INFO