Intersection of automorph-conjugate subgroups
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
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 |