SMOOTH UNIONS OF BUTLER GROUPS

If G = boolean OR(alpha<kappa)G(alpha) is the union of a smooth strict ly ascending chain of B-2-subgroups G(alpha), then, in the case when k appa < N-omega, a criterion is established under which G becomes a B-2 -group. This criterion is dependent on a new class of torsion-free gro ups and generalizes earlier criteria for freeness established by Paul Hill. The result of S. Shelah and others establishing that, for a weak ly compact cardinal kappa ''kappa-free'' implies ''free'', is extended to the case of B-2-groups.