We characterize finite groups having a cyclic Sylow p-subgroup in terms of the action of a specific Galois automorphism on the principal p-block for p=2,3. We show that the analog statement for blocks with arbitrary defect group would follow from the blockwise McKay-Navarro conjecture.

中文翻译：

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主块和循环 Sylow 子群上的伽罗瓦作用

我们根据特定伽罗瓦自同构对 p=2,3 的主 p 块的作用来表征具有循环 Sylow p 子群的有限群。我们表明，具有任意缺陷组的块的模拟陈述将遵循块状 McKay-Navarro 猜想。