Torsion-free abelian group

Definition
A torsion-free abelian group or aperiodic abelian group or locally free abelian group is a group satisfying the following equivalent conditions:


 * 1) It is both an abelian group and a torsion-free group, i.e., no non-identity element of the group has finite order.
 * 2) Every finitely generated subgroup of it is a defining ingredient::free abelian group.