QUASI-ISOMORPHISMS AND GROUPS OF QUASI-HOMOMORPHISMS.

This paper investigates to which extent a self-small mixed Abelian group G of finite torsion-free rank is determined by the groups Hom(G,C) where C is chosen from a suitable class $\mathcal C$ of Abelian groups. We show that G is determined up to quasi-isomorphism if $\mathcal C$ is the class of all self-small mixed groups C with r0(C) ≤ r0(G). Several related results are given, and the dual problem of orthogonal classes is investigated. [ABSTRACT FROM AUTHOR]