We determine the structure of ap-pure[pure] hull of ap-purifiable [purifiable] subgroup of an arbitrary abelian group. Moreover, we prove that a subgroupAof an abelian groupGis purifiable inGif and only ifAisp-purifiable inGfor every primep. Using these results, we characterize the groupsGfor which all subgroups are purifiable inG. Furthermore, we establish several properties of purifiable subgroups.