The radical of the center of a group algebra

Abstract:

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