Periodic abelian group

Definition
A periodic abelian group (also called torsion abelian group or abelian torsion group or locally finite abelian group) is a group satisfying the following equivalent conditions:


 * 1) It is both a locally finite group and an abelian group.
 * 2) it is both a periodic group (i.e., every element has finite order) and an abelian group.
 * 3) It is both an abelian group and a group generated by periodic elements.
 * 4) When it is endowed with the discrete topology, its Pontryagin dual is an abelian profinite group.