Cancellation properties for quotient divisible groups

Abstract

We investigate cancellation, the unit lifting property, and 1 in the stable range for mixed self-small abelian groups of finite torsion-free rank. Some of our results generalize results previously obtained for torsion-free finite rank groups by Fuchs, Kravchenko, Loonstra, and Stelzer. In particular, we prove Stelzer's main cancellation result for the class of mixed quotient divisible abelian groups.