On some rational extension properties for $GL_n(q)$ and even-degree characters fixed by order-2 Galois automorphisms
Group Theory
2022-12-16 v2 Representation Theory
Abstract
In this note, we prove that if every character of a finite group fixed by an order-2 Galois automorphism has odd degree, then has a normal Sylow -subgroup. On the way, we study extensions of characters of , odd, to the group extended by the transpose-inverse automorphism and prove that unipotent characters of extend to rational characters of its automorphism group.
Keywords
Cite
@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}
}
Comments
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 Withdrawn until I obtain a working solution