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.