## H. Pat Goeters, William Ullery

*Quasi-balanced torsion-free groups *

Comment.Math.Univ.Carolinae 39,3 (1998) 431-443. **Abstract:**An exact sequence $0\to A\to B\to C\to 0$ of torsion-free abelian groups is quasi-balanced if the induced sequence $$ 0\to \bold Q\otimes Hom(X,A)\to \bold Q\otimes Hom(X,B) \to \bold Q\otimes Hom(X,C)\to 0 $$ 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 from balanced sequences. As an application of our results concerning quasi-balanced sequences, the relationship between the two chains in the quasi-category of torsion-free abelian groups is illuminated.

**Keywords:** quasi-balanced, almost balanced, Kravchenko classes

**AMS Subject Classification:** 20K15

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