Donovan's conjecture and extensions by the centralizer of a defect group

2020/06/19 by Eaton, Charles W., Livesey, Michael
#20C20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2006.11173

Abstract

We consider Donovan's conjecture in the context of blocks of groups G with defect group D and normal subgroups N \lhd G such that G=C_D(D∩ N)N, extending similar results for blocks with abelian defect groups. As an application we show that Donovan's conjecture holds for blocks with defect groups of the form Q₈ × C_2ⁿ or Q₈ × Q₈ defined over a discrete valuation ring.

Related

• Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings
• Donovan's conjecture and blocks with abelian defect groups
• Towards Donovan's conjecture for abelian defect groups
• 2-blocks with abelian defect groups
• Morita equivalence classes of blocks with extraspecial defect groups p₊¹⁺²