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arXiv · 2212.04536

On some rational extension properties for $GL_n(q)$ and even-degree characters fixed by order-2 Galois automorphisms

A. A. Schaeffer Fry
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Abstract

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.

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BibTeXRIS

A. A. Schaeffer Fry. 2022-12-08. On some rational extension properties for $GL_n(q)$ and even-degree characters fixed by order-2 Galois automorphisms. https://arxiv.org/abs/2212.04536

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