Projective and injective Butler groups. (English) Zbl 0663.20059

A Butler group is a pure subgroup of a torsion free completely decomposable abelian group of finite rank. The class of all Butler groups is a torsion free class. The author characterizes the projectives and injectives in the category of all Butler groups and shows that only the semi-local ones have an injective resolution and only the free ones have a projective resolution. The subclass of Butler groups with typesets contained in a finite sublattice of the lattice of types is considered. It is shown that unlike in the category of quasi-homomorphisms there are not necessarily enough projectives and injectives.
Reviewer: J.Hausen


20K40 Homological and categorical methods for abelian groups
20K15 Torsion-free groups, finite rank