The radical of the center of a group algebra

Abstract

Let K [ G ] K[G] denote the group algebra of a finite group G over a field K of characteristic p > 0 p > 0 and let Z = Z ( K [ G ] ) \mathcal {Z} = {\mathbf {Z}}(K[G]) . In this paper, we offer a bound for the nilpotence degree of the Jacobson radical J Z J\mathcal {Z} in terms of the order of a Sylow p-subgroup of G.