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.

中文翻译：

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Donovan的猜想和缺陷群扶正器的扩展

我们在具有缺陷组D和正常子组的G组块的上下文中考虑Donovan猜想$ñ◁G$ 这样 $G=C_d（d\cap ñ）ñ$，扩展了具有阿贝尔缺陷组的块的相似结果。作为一个应用，我们证明了多诺万猜想对具有以下缺陷组形式的块成立${问}_8\times C_{{\mathrm{2个}}^{ñ}}$ 或者 ${问}_8\times {问}_8$ 在离散估值环上定义。