Blocks whose defect groups are Suzuki 2-groups

Abstract

We classify up to Morita equivalence all blocks whose defect groups are Suzuki 2-groups. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field, and in fact holds up to basic Morita equivalence. As a consequence Donovan's conjecture holds for Suzuki 2-groups. A corollary of the proof is that Suzuki Sylow 2-subgroups of finite groups with no nontrivial odd order normal subgroup are trivial intersection.