Quotient divisible abelian groups

Abstract

An abelian group G G is called quotient divisible if G G is of finite torsion-free rank and there exists a free subgroup F ⊂ G F\subset G such that G / F 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 G \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 G \mathcal {G} coincides with the duality previously constructed by the authors.