Abelian implies every subgroup is normal
From Groupprops
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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Contents
Statement
Verbal statement
Every subgroup of an Abelian group is a normal subgroup.
Propertytheoretic statement
The group property of being an Abelian group is stronger than the group property of being a Dedekind group (a group where every subgroup is normal).