We determine the structure of a $p$-vertical[vertical] subgroup $A$ of an arbitrary abelian group $G$ such that every neat hull of $A$ is $p$-purifiable[purifiable] in $G$.
"On kernels of purifiability in arbitrary abelian groups." Hokkaido Math. J. 30 (1) 177 - 194, February 2001. https://doi.org/10.14492/hokmj/1350911930