Are the groups $(\Bbb Q^2,+)$ and $(\Bbb Q,+)$ isomorphic ?
I don't know how to proceed because I am getting all the structural properties same.
Can I get some help?
2026-03-26 12:13:32.1774527212
Are the groups $(\Bbb Q^2,+)$ and $(\Bbb Q,+)$ isomorphic?
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A key property of $\mathbb{Q}$ as an additive group: any two nonzero elements are commensurable. That is, for any nonzero $a,b$, they are both integer multiples of some common divisor $c$.
This is not true of $\mathbb{Q}^2$; $(1,0)$ and $(0,1)$ are incommensurable.
Therefore, the two groups are not isomorphic.