Nilpotency indices of the radicals of finite p-solvable group algebras, I

Abstract

AbstractLet k be a field of characteristic p > 0, G a finite p-solvable group and pm the highest power of p dividing the order of G. We denote by t(G) the nilpotency index of the (Jacobson) radical of the group algebra k[G]. The groups G with t(G) ≥ pm−1 are already classified. The aim of this paper is to classify the p-solvable groups G with pm−2 < t(G) < pm−1 for p odd.