Broué's abelian defect group conjecture for the Held group and the sporadic Suzuki group

Abstract

In representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an abelian defect group P, then A and its Brauer corresponding p-block B of N G ( P) are derived equivalent. We demonstrate in this paper that Broué's conjecture holds for non-principal 3-blocks A with elementary abelian defect group P of order 9 of the simple Held group and the sporadic simple Suzuki group.