Quotient divisible abelian groups

An abelian group $G$ is called quotient divisible if $G$ is of finite torsion-free rank and there exists a free subgroup $F\subset G$ such that $G/F$ is divisible. The class of quotient divisible groups contains the torsion-free finite rank quotient divisible groups introduced by Beaumont and Pierce and essentially contains the class $\mathcal{G}$ of self-small mixed groups which has recently been investigated by several authors. We construct a duality from the category of quotient divisible groups and quasi-homomorphisms to the category of torsion-free finite rank groups and quasi-homomorphisms. Our duality when restricted to torsion-free quotient divisible groups coincides with the duality of Arnold and when restricted to $\mathcal{G}$ coincides with the duality previously constructed by the authors.