$\fbox{1}$ Prove that any finitely generated subgroup of $(\mathbb{Q},+)$ is cyclic.
$\fbox{2}$ Prove that $\mathbb{Q}$ is not isomorphic to $\mathbb{Q}\times \mathbb{Q}$.
Any hints would be appreciated.
$\fbox{1}$ Prove that any finitely generated subgroup of $(\mathbb{Q},+)$ is cyclic.
$\fbox{2}$ Prove that $\mathbb{Q}$ is not isomorphic to $\mathbb{Q}\times \mathbb{Q}$.
Any hints would be appreciated.