BUTLER GROUPS OF INFINITE RANK

Butler groups are torsion-free abelian groups which - in the infinite rank case - can be defined in two different ways. One definition requi res that all the balanced extensions of torsion groups by them are spl itting, while the other stipulates that they admit continuous transfin ite chains (with finite rank factors) of so-called decent subgroups. T his paper is devoted to the three major questions for Butler groups of infinite rank: Are the two definitions equivalent? Are balanced subgr oups of completely decomposable torsion-free groups always Butler grou ps? Which pure subgroups of Butler groups are again Butler groups? In attacking these problems, a new approach is used by utilizing N0-preba lanced chains and relative balanced-projective resolutions introduced by Bican and Fuchs [5]. A noteworthy feature is that no additional set -theoretical hypotheses are needed.