On the nilpotency index of the radical of a group algebra

Abstract

Throughout the present note, K will represent an algebraically closed field of characteristic p>0. In case G is a p-solvable group of order p^{a}m (a\geqq 1,p\parallel m) , concerning the nilpotency index t(G) of the radical J(KG) of the group algebra KG, D. S. Passman [4 ; Th. 1. 6], Y. Tsushima [5; Th.2] and D. A. R. Wallace [7; Th. 3. 3] have obtained the following: p^{a}\geqq t(G)\geqq a(p-1)+1 .