Broué's Abelian defect group conjecture for the Held group and the sporadic Suzuki group. (Q1880687)

The Broué conjecture in representation theory states 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. In the present paper the authors verify the Broué conjecture for non-principal 3-blocks \(A\) with elementary Abelian defect group \(P\) of order \(9\) in the sporadic simple groups \(He\) and \(Suz\).