Abelian automorphism group not implies cyclic
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., group whose automorphism group is abelian) need not satisfy the second group property (i.e., cyclic group)
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- Locally cyclic implies abelian automorphism group, locally cyclic not implies cyclic
- Abelian and abelian automorphism group not implies locally cyclic
- Abelian automorphism group not implies abelian, cyclic implies abelian
We can counterexamples generated from Fact (1), (2), or (3).