Abelian implies every subgroup is potentially characteristic
This article gives the statement and possibly, proof, of an implication relation between two subgroup properties, when the big group is a abelian group. That is, it states that in a Abelian group (?), every subgroup satisfying the first subgroup property (i.e., Subgroup (?)) must also satisfy the second subgroup property (i.e., Potentially characteristic subgroup (?)). In other words, every subgroup of abelian group is a potentially characteristic subgroup of abelian group.
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This fact is related to: NPC conjecture
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- Finite implies every normal subgroup is potentially characteristic
- Nilpotent implies every normal subgroup is potentially characteristic
- Hypercentral implies every normal subgroup is potentially characteristic
The proof follows directly by piecing together facts (1) and (2).