论文标题
在某些合理扩展属性上，用于$ gl_n（q）$甚至
On some rational extension properties for $GL_n(q)$ and even-degree characters fixed by order-2 Galois automorphisms
论文作者
论文摘要
在本说明中，我们证明，如果由订单2 Galois自动形态固定的有限组$ G $的每个字符具有奇怪的学位，则$ G $具有正常的Sylow $ 2 $ -subgroup。在途中，我们将$ gl_n（q）$，$ q $奇数的字符的扩展扩展到由跨置式式自动形态学扩展到的组，并证明$ psl_n（q）$的一单位性字符扩展到其自动形态群体的理性字符。
In this note, we prove that if every character of a finite group $G$ fixed by an order-2 Galois automorphism has odd degree, then $G$ has a normal Sylow $2$-subgroup. On the way, we study extensions of characters of $GL_n(q)$, $q$ odd, to the group extended by the transpose-inverse automorphism and prove that unipotent characters of $PSL_n(q)$ extend to rational characters of its automorphism group.
