Broué's conjecture for 2-blocks with elementary abelian defect groups of order 32

Abstract

The first author recently classified the Morita equivalence classes of 2-blocks of finite groups with elementary abelian defect groups of order 32. In all but three cases he proved that the Morita equivalence class determines the inertial quotient of the block. We finish the remaining cases by utilizing the theory of lower defect groups. As a corollary, we verify Broué’s Abelian Defect Group Conjecture in this situation.

Keywords

• 2-block
• morita equivalence
• abelian defect group
• broué’s conjecture