On a class of locally Butler groups. (English) Zbl 0748.20029

Bican, Ladislav

Commentat. Math. Univ. Carol. 32, No. 4, 597-600 (1991).

A torsion-free abelian group \(G\) is called a Butler group if \(\text{Bext}(G,T)=0\) for any torsion group \(T\). It is an open question whether a finite rank pure subgroup of a Butler group is again Butler. The author shows that this is indeed the case if \(G\) is a smooth union of an ascending chain of pure subgroups \(G_ \alpha\) each of which has its typeset at most countable.

Reviewer: K.M.Rangaswamy (Colorado Springs)

MSC:

20K20	Torsion-free groups, infinite rank
20K27	Subgroups of abelian groups
20K35	Extensions of abelian groups

Keywords:

torsion-free abelian group; Butler group; finite rank pure subgroup; smooth union; ascending chain of pure subgroups; typeset