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

We consider Donovan's conjecture in the context of blocks of groups G with defect group D and normal subgroups N (sic) G such that G = C-D(D boolean AND 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 Q(8) x C-2n or Q(8) x Q(8) defined over a discrete valuation ring. (C) 2021 The Authors. Published by Elsevier Inc.