ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16, 20 Ninomiya, Yasushi, Sinshu University, Japan Group algebras and nilpotency indices of their radicals The (Jacobson) radical J(k[G]) of the group algebra k[G] of a finite group G over a field k is a nilpotent ideal. The nilpotency index, say t(G), of J(k[G]) is the least positive integer t such that J(k[G′])^{t} = 0. For finite p-solvable groups G, will be presented. Further, an example of a finite p-solvable group G with t(G) > t(P), where P is a Sylow p-subgroup of G, will be presented. The existence of such p-solvable groups is probably unknown.