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Somebody told me there exists a torsion-free abelian group $G$, such that $G$ is isomorphic to $G\oplus G\oplus G$, but $G$ is not isomorphic to $G\oplus G$. But he does not tell me such a concrete example, since he dose not know too.

I do not know if there is a well-known example about this. Could anyone give such an example? Or any references?


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I think such an example is due to ALS Corner. – Geoff Robinson Jul 8 '11 at 10:15
If you have access to mathscinet or Maths Reviews, try MR0169905, where a much more general result is given. – Geoff Robinson Jul 8 '11 at 10:25
up vote 6 down vote accepted

As Geoff Robinson mentioned, you may find it here

P.S. I don't know why I cannot write a comment now. Something is wrong with my PC!

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