On centers of blocks with non-cyclic defect groups

Abstract

In this short note we study the center ZB of a block B of a finite group over an algebraically closed field of prime characteristic through its Loewy length llZB. A result of Okuyama in 1981 gave an upper bound for llZB in terms of defect group of B. The purpose of this note is to improve this bound for non-cyclic defect groups.

3 pages