Note on quasi-isomorphism of torsion free abelian groups of finite rank (Preliminary communication)

Ladislav Procházka

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An exact sequence $0 \to A \to B \to C \to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $0 \to 𝐐 \otimes Hom (X, A) \to 𝐐 \otimes Hom (X, B) \to 𝐐 \otimes Hom (X, C) \to 0$ is exact for all rank-1 torsion-free abelian groups $X$ . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which $C$ is a Butler group. The special case where $B$ is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise...