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For instance consider the group $G = \{1 , -1 , i, -i\}$ , it is a cyclic group of order 4 and it is abelian as well but 4 is not a square free number so how does the above theorem holds true ?

Stefan4024
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Radha Gogia
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    Where did you find this "theorem"? For any number $n$, the cyclic group on $n$ elements is abelian – TomGrubb Jul 03 '17 at 17:44
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    What makes you think that this is a theorem? You have one counterexample already, the cyclic group of order $n^2$ is a whole family. – lulu Jul 03 '17 at 17:44

1 Answers1

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I think you're confusing this statement with its converse. See this question: Square free finite abelian group is cyclic

What is true is the following:

If an abelian group has squarefree order, then it is cyclic.

See the linked question for a proof.

aras
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