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Abelian automorphism group not implies cyclic

666 bytes added, 23:32, 20 June 2013
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{{group property non-implication|stronger = group whose automorphism group is abelian|weaker = cyclic group}} ==Statement== It is possible to have a [[group whose automorphism group is abelian]] but such that the group is not a [[cyclic group]]. ==Related facts== ===Opposite facts=== * [[finite abelian and abelian automorphism group implies cyclic]] ==Facts used== # [[uses::Locally cyclic implies abelian automorphism group]], [[uses::locally cyclic not implies cyclic]]#redirect [[uses::Abelian and abelian automorphism group not implies locally cyclic]]# [[uses::Abelian automorphism group not implies abelian]], [[uses::cyclic implies abelian]] ==Proof== We can counterexamples generated from Fact (1), (2), or (3).
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