TORSION-FREE EXTENSIONS OF BUTLER GROUPS BY PRIMARY GROUPS

The class of those abelian p-groups T is characterized for which every torsion-free group G with T congruent-to G/B is a B2-group whenever t he subgroup B is a B2-group. This class of p-groups turns out to be th e same as the class obtained by Dugas and Irwin [4] who dealt with the analogous problem for free (rather than B2-)groups. It is also shown that the totally reduced p-groups (defined below) belong to the class of p-groups under consideration.