Butler groups and Bext: A constructive view. (English) Zbl 0777.20022

Mines, R.; Vinsonhaler, C.

Abelian groups and noncommutative rings, Collect. Pap. in Mem. of R. B. Warfield jun., Contemp. Math. 130, 289-299 (1992).

[For the entire collection see Zbl 0745.00066.]
The authors use the constructive approach to study the pure subgroups of finite rank completely decomposable groups which are also known as the Butler groups. The key point of this paper is a constructive proof of a classical theorem of L. Bican [Czech. Math. J. 28(103), 356-364 (1978; Zbl 0421.20022)] that a finite rank torsion-free abelian group \(G\) is Butler if and only if, for any torsion group \(T\), every balanced exact sequence \(0\to T\to H\to G\to 0\) splits.

Reviewer: K.M.Rangaswamy (Colorado Springs)

MSC:

20K15	Torsion-free groups, finite rank
20K35	Extensions of abelian groups
20K27	Subgroups of abelian groups

Keywords:

pure subgroups; finite rank completely decomposable groups; Butler groups; finite rank torsion-free abelian group; balanced exact sequence

Citations:

Zbl 0745.00066; Zbl 0421.20022