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]

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 Automorph-conjugate subgroup|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