Abelian implies ACIC

Property-theoretic statement
The group property of being an Abelian group is stronger than the group property of being an ACIC-group.

Verbal statement
Any Abelian group is ACIC: any automorph-conjugate subgroup is characteristic.

Intermediate properties

 * Dedekind group: This is a group where every subgroup is normal, although the group is not necessarily Abelian.

Related facts

 * Dedekind implies ACIC
 * ACIC implies nilpotent (finite groups)
 * Frattini subgroup is ACIC