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

Charles W. Eaton; Michael Livesey

paper

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

arXiv:2006.11173

Abstract

We consider Donovan's conjecture in the context of blocks of groups $G$ with defect group $D$ and normal subgroups $N ⊲ G$ such that $G = C_{D} (D \cap N) N$ , 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 $Q_{8} \times C_{2^{n}}$ or $Q_{8} \times Q_{8}$ defined over a discrete valuation ring.