We prove that for all non-abelian finite simple groups S, there exists a fake mth Galois action on IBr(X) with respect to X ◃ X ⋊ Aut(X), where X is the universal covering group of S and m is any non-negative integer coprime to the order of X. This is one of the two inductive conditions needed to prove an ℓ-modular analogue of the Glauberman–Isaacs correspondence.

中文翻译：

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假伽罗瓦动作

我们证明对于所有非阿贝尔有限单群小号, 存在假的米th 伽罗瓦行动溴化溴(X)关于X ◃ X ⋊ 自动(X)， 在哪里X是的全覆盖群小号和米是任何非负整数互质数的顺序X. 这是证明一个ℓ-格劳伯曼-艾萨克对应的模模拟。