Butler groups of arbitrary cardinality (Q1310165)

In 1990 M. Dugas, P. Hill and K. M. Rangaswamy proved that under the continuum hypothesis the classes of Butler (\(= B_ 1\)) and \(B_ 2\)- groups coincide up to the cardinality \(\aleph_ \omega\). The main result of this paper is the proof of the coincidence of these two classes in the constructible universe without cardinality restrictions. As a by-product the authors obtain several results on chains and axiom-3 families of separative subgroups. Moreover, under \((V = L)\) \(\text{Bext}^ 2(G,T) = 0\) for all torsionfree groups \(G\) and torsion groups \(T\).