Dedekind not implies abelian
This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., Dedekind group) need not satisfy the second group property (i.e., Abelian group)
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In fact, the quaternion group is in some sense the only counterexample: any non-Abelian Dedekind group is a direct product of the quaternion group and an Abelian group with the Abelian group satisfying certain conditions.