A group $G$ is locally cyclic if whenever $H \le G$ is a finitely generated subgroup then $H$ is cyclic. If $G$ is a locally cyclic group then $G$ is isomorphic to a quotient of a subgroup of the rational numbers under addition. An online proof of this fact appears at groupprops. However, despite some searching, I have been unable to find a proof in the published literature on abelian groups.
Is there a published paper or textbook that has a proof that every locally cyclic group is isomorphic to a quotient of a subgroup of the rational numbers?