An equivalence relation for torsion-free Abelian groups of finite rank
The equivalence relation in question is defined as follows: let \({^\perp G}=\{X:\Hom(X,G)=0\}\). Then \(G\) is equivalent to \(H\) if and only if \({^\perp G}={^\perp H}\). Since this relation is coarser than quasi-isomorphism, it is useful in classifying torsion-free abelian groups. The author finds several closure properties of the relation, and an intrinsic characterisation of the equivalence classes. The main result is a classification of those finite rank groups for which equivalence and equality of rank imply quasi-isomorphism. A subsequent paper [\textit{P. Schultz, C. Vinsonhaler} and \textit{W. J. Wickless}, J. Aust. Math. Soc., Ser. A 52, No. 1, 119-129 (1992; Zbl 0784.20027)] develops further properties of the relation.
scientific article; zbMATH DE number 130480