On a Filtered Multiplicative Bases of Group Algebras II

We give an explicit list of all p-groups G with a cyclic subgroup of index p ², such that the group algebra KG over the field K of characteristic p has a filtered multiplicative K-basis. We also prove that such a K-basis does not exist for the group algebra KG, in the case when G is either a non-Abelian powerful p-group or a two generated p-group (p2) with a central cyclic commutator subgroup. This paper is a continuation of the paper which appeared in Arch. Math. (Basel) 74 (2000), 217–285.