On a filtered multiplicative basis of group algebras

Let K be a field of characteristic p and G a nonabelian metacyclic finite p -group. We give an explicit list of all metacyclic p-groups G, such that th e group algebra KG over a field of characteristic p has a filtered multipli cative K-basis. We also present an example of a non-metacyclic 2-group G, s uch that the group algebra KG over any field of characteristic 2 has a filt ered multiplicative K-basis.