Broué's conjecture for the nonprincipal block of [formula omitted] with full defect

Abstract

M. Broué gives an important conjecture which is called Broué's abelian defect group conjecture. This conjecture says that a p-block, where p is a prime number, of a finite group with an abelian defect group is derived equivalent to its Brauer correspondent in the normalizer of the defect group. In this paper, we prove that this conjecture is true for the nonprincipal block of SL ( 2 , p n ) for a positive integer n.