Let $b$ be a block with normal abelian defect group and abelian inertial quotient. We prove that every Morita auto-equivalence of $b$ has linear source. We note that this improves upon results of Zhou and Boltje, Kessar and Linckelmann. We also prove that $\operatorname{Picent}(b)$ is trivial which is conjectured to be the case for all blocks.

中文翻译：

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关于具有正常缺陷组的 Picard 块组

令 $b$ 是一个具有正常阿贝尔缺陷群和阿贝尔惯性商的块。我们证明 $b$ 的每个 Morita 自动等价物都有线性源。我们注意到这比 Zhou 和 Boltje、Kessar 和 Linckelmann 的结果有所改进。我们还证明 $\operatorname{Picent}(b)$ 是微不足道的，推测所有块的情况都是如此。