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> Show that $(\mathbb{Z}\_{n} \times \mathbb{Z}\_{n} , +)$ is not isomorphic to $ (\mathbb{Z}\_{n^{2}} , +)$
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I know that isomorphism preserves the order.
In the first group there is no element of order $n^{2}$ but there is in the second group. So these groups are not isomorphic. 

I think I am right. Is there another way to solve this problem?