Broué's conjecture for the nonprincipal block of SL(2,q) with full defect

Abstract

Communicated by Michel Broué Keywords: Broué's abelian defect group conjecture Derived equivalence Tilting complex Stable equivalence of Morita type 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.