A remark on the Loewy-layers of the modular group algebra of a finite p-group

Abstract

We consider the dimensions c i of the Loewy factors of the modular group algebra KG of a finite p-group G. It is well-known that c i = c s−i where s is the Loewy length of KG. For p = 3 and 5 we describe p-groups with the property that c i ⩽ c i−1 for some i⩽ 1 2 S thus settling an old open problem. Also, the similar question for restricted Lie algebras with nilpotent p-map is studied.