Central ideals and Jacobson radicals of blocks of group algebras

Abstract

We study the relationship between the central ideals and the Jacobson radicals of blocks of group algebras. In particular, we characterize the blocks with the property that the square of the radical is a non-zero central ideal. Moreover, we also consider the blocks with the property that the cube of the radical becomes a non-zero central ideal. These are improvements of a result by Külshammer in 2020.