# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 42 (2013) pp.331-343

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### Abstract

First we introduce the concept of QD-hulls in arbitrary abelian groups. Then we use the concept to give a new characterization of purifiable torsion-free finite rank subgroups of an arbitrary abelian group. Finally we use it to formulate a splitting criterion for mixed groups of torsion-free finite rank.

MSC(Primary) 20K21 20K27 Splitting mixed group, QD-hull, purifiable subgroup, vertical subgroup, N-high subgroup, n-th p-overhang