Abelian implies ACIC
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This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property must also satisfy the second group property
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Statement
Propertytheoretic statement
The group property of being an Abelian group is stronger than the group property of being an ACICgroup.
Verbal statement
Any Abelian group is ACIC: any automorphconjugate subgroup is characteristic.
Definitions used
Abelian group
Further information: Abelian group
ACICgroup
Further information: ACICgroup
Intermediate properties
 Dedekind group: This is a group where every subgroup is normal, although the group is not necessarily Abelian.