## Countable Butler groups.(English)Zbl 0769.20025

Abelian groups and noncommutative rings, Collect. Pap. in Mem. of R. B. Warfield jun., Contemp. Math. 130, 133-143 (1992).
[For the entire collection see Zbl 0745.00066.]
The authors start with the homological study of prebalanced exact sequences. An important result asserts that any prebalanced extension of a torsion group by a torsionfree one is balanced (Thm. 1.5). The next part presents a simple proof of a result of Dugas and Rangaswamy that characterizes the finite corank TEP-subgroups of countable Butler groups as prebalanced subgroups with Butler factor (Thm. 2.2). This leads in the last two sections to the proofs of the coincidence of the classes of finitely Butler, $$B_ 1$$ and $$B_ 2$$-groups in the finite and countable rank cases.
Reviewer: L.Bican (Praha)

### MSC:

 20K20 Torsion-free groups, infinite rank 20K40 Homological and categorical methods for abelian groups 20K35 Extensions of abelian groups 20K27 Subgroups of abelian groups

### Biographic References:

Warfield, R. B. jun.

Zbl 0745.00066