Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Chiba-city, 263, Japan
Abstract:
We give a result on Cartan invariants of the group algebra of a finite group over an algebraically closed field , which implies that if the Loewy length (socle length) of the projective indecomposable -module corresponding to the trivial -module is four, then has characteristic 2. The proof is independent of the classification of finite simple groups.