On the radical of the group algebra of a symmetric group

摘要

Let A = Z(p)S(n) with p a prime and S-n a symmetric group. We prove in this paper that if n < 2p, then radA = I, where I is the nilpotent ideal constructed in Radicals of symmetric cellular algebras, Collog. Math. 133 (2013) 67-83. Finally we give two remarks on algebras A = Z(p)S(n) with n < 2p.