On filtered multiplicative bases of group algebras II

Abstract

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 proved that such a K-basis does not exist for the group algebra KG, in the case when G$ is either a powerful p-group or a two generated p-group (p\not=2) with a central cyclic commutator subgroup. This paper is a continuation of the related V. Bovdi, On a filtered multiplicative basis of the group algebras Arch. Math. (Basel) 74 (2000) 81--88