We study fields of values of the restriction to Sylow subgroups of irreducible characters of the normalizers of Sylow subgroups in symmetric and alternating groups. As an application, we show that these classes of groups admit a McKay bijection that respects fields of values and restriction to Sylow subgroups.

中文翻译：

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对称群和交替群的 McKay 双射

我们研究对称和交替群中 Sylow 子群的归一化器的不可约特征对 Sylow 子群的限制值域。作为一个应用，我们展示了这些群类承认一个 McKay 双射，它尊重值域和对 Sylow 子群的限制。