Locally cyclic torsion-free group

Definition
A group is termed a locally cyclic torsion-free group if it satisfies the following equivalent conditions:


 * 1) It is both a locally cyclic group (i.e., every finitely generated subgroup is cyclic) and a torsion-free group (i.e., no non-identity element has finite order).
 * 2) It is isomorphic to a subgroup of the defining ingredient::group of rational numbers.