Let $G$ be an arbitrary group. A subgroup $A$ of $G$ is purifiable in $G$ if, among the pure subgroups of $G$ containing $A$, there exists a minimal one. We studied purifiable subgroups of abelian groups in . In this note, we give simple proofs of [4,Theorem 4.6], [4,Theorem 4.7], and [4,Theorem 4.8].
"Purifiable Subgroups II." Hokkaido Math. J. 34 (1) 237 - 245, February 2005. https://doi.org/10.14492/hokmj/1285766206