How to show that the group $(G,+)$ is abelian and I already proved that $(0,0)$ is a neutral element of addition and this is the givings $G=\mathbb{Q} \times \mathbb{Z}$ with operations $(a,b)+(c,b)=(a+c , b+d)$
2026-02-22 17:57:04.1771783024
how to show that the group $(G,+)$ is abelian
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If both factors in the direct product are abelian, so is the direct product. Indeed
$$(a,b) + (c,d) = (a+c,b+d) = (c+a,b+d) = (c,d) + (a,b)$$