Morita equivalence classes of blocks with elementary abelian defect groups of order 32

Abstract

We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.

32 pages. Removed Prop. 5.4 due to an incomplete proof (the result will appear in a subsequent paper)

References in corpus (1)

• Nilpotent extensions of blocks

Cited by in corpus (3)

• Morita equivalence classes of $2$-blocks with abelian defect groups of rank $4$
• 2-blocks with an abelian defect group and a freely acting cyclic inertial quotient
• $2$-Blocks whose defect group is homocyclic and whose inertial quotient contains a Singer cycle II