NILPOTENCY INDICES OF THE RADICALS OF FINITE p-SOLVABLE GROUP ALGEBRAS. II

Abstract

ABSTRACT In [6], we have classified the p -solvable groups G with for p odd, where is the nilpotency index of the (Jacobson) radical of , k a field of characteristic p , and the highest power of p dividing the order of G . In the paper cited above, we have given only an outline of the proof of the result for p=3 ([[6], Theorem 11]). One of the aims of this paper is to give the complete proof of part (2) in the theorem. The other one is to show that the 3-solvable group G discussed in this paper satisfies the inequality , where P is a Sylow 3-subgroup of G . This is probably the first example satisfying this property. Further we correct errors in [5].