关于GL_n(q)的若干有理扩张性质及被2阶伽罗瓦自同构固定的偶次特征标
群论
2022-12-16 v2 表示论
摘要
在本注记中，我们证明：若有限群的每一个被2阶伽罗瓦自同构固定的特征标均有奇次数，则有一个正规Sylow -子群。在此过程中，我们研究当为奇数时的特征标到由转置逆自同构扩张所得群的扩张，并证明的幂单特征标可扩张为其自同构群的有理特征标。
引用
@article{arxiv.2212.04536,
title = {On some rational extension properties for $GL_n(q)$ and even-degree characters fixed by order-2 Galois automorphisms},
author = {A. A. Schaeffer Fry},
journal= {arXiv preprint arXiv:2212.04536},
year = {2022}
}
备注
Thm. A, Cor. B, are incorrect as stated and would require additional assumptions on q (a result of a missing assumption in another paper). Withdrawn until I obtain a working solution