The class of those abelian p-groups T is characterized for which every torsion-free group G with T= G/B is a B2-group whenever the subgroup B is a B2-group. This class of p-groups turns out to be the 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