Displaying similar documents to “Quasi-isomorphism and ℤ ( 2 ) -representations for a class of Butler groups”

On direct sums of ℬ ( 1 ) -groups

Claudia Metelli (1993)

Commentationes Mathematicae Universitatis Carolinae

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A necessary and sufficient condition is given for the direct sum of two ℬ ( 1 ) -groups to be (quasi-isomorphic to) a ℬ ( 1 ) -group. A ℬ ( 1 ) -group is a torsionfree Abelian group that can be realized as the quotient of a finite direct sum of rank 1 groups modulo a pure subgroup of rank 1.

Quasi-balanced torsion-free groups

H. Pat Goeters, William Ullery (1998)

Commentationes Mathematicae Universitatis Carolinae

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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...