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Quasi-balanced torsion-free groups

H. Pat Goeters, William Ullery (1998)

Commentationes Mathematicae Universitatis Carolinae

An exact sequence 0 A B C 0 of torsion-free abelian groups is quasi-balanced if the induced sequence 0 𝐐 Hom ( X , A ) 𝐐 Hom ( X , B ) 𝐐 Hom ( X , C ) 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...

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