# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 34 (2005) pp.237-245

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### Abstract

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 [4]. In this note, we give simple proofs of [4,Theorem 4.6], [4,Theorem 4.7], and [4,Theorem 4.8].

MSC(Primary) 20K21 20K27 almost-dense subgroup, p-purifiable subgroup, purifiable subgroup, poverhang set, torsion-complete