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

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.

Definitions used

Abelian group

Further information: Abelian group

ACIC-group

Further information: ACIC-group

Intermediate properties

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

Related facts