Pure subgroups of Butler groups. (English) Zbl 0569.20045

Bican, Ladislav

Abelian groups and modules, Proc. Conf., Udine/Italy 1984, CISM Courses Lect. 287, 203-213 (1984).

[For the entire collection see Zbl 0552.00004.]
A torsionfree abelian group H is called a Butler group if \(Bext(H,T)=0\) for all torsion groups T, where Bext is the subfunctor of Ext consisting of the equivalence classes of the balanced exact sequences. The author shows that the class of Butler groups with inversely well-ordered type- set is closed under pure subgroups. It is furthermore shown that a homogeneous torsionfree group is Butler, if and only if it is completely decomposable.

Reviewer: P.Gräbe

MSC:

20K20	Torsion-free groups, infinite rank
20K35	Extensions of abelian groups
20K27	Subgroups of abelian groups
20K25	Direct sums, direct products, etc. for abelian groups

Keywords:

torsionfree abelian group; balanced exact sequences; Butler groups; type- set; pure subgroups; homogeneous torsionfree group; completely decomposable

Citations:

Zbl 0552.00004