Towards Donovan's conjecture for abelian defect groups

2017/11/14 by Eaton, Charles, Livesey, Michael
#20C20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1711.05357

Abstract

We define a new invariant for a p-block, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64.

Related

• Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings
• Donovan's conjecture and blocks with abelian defect groups
• Donovan's conjecture and extensions by the centralizer of a defect group
• The strong Frobenius numbers for cyclic defect blocks are equal to one
• Blocks with normal abelian defect and abelian p' inertial quotient