Year: 2026
Type: preprint
Abstract: We show that if $G$ is a finite solvable group such that $E = \mathbb Q(\{χ(g)\, |\, χ\in{\rm Irr}(G),\ g \in G\})$ is an extension of degree 2 over the rationals, then $E = \mathbb Q(\sqrt{\pm d})$ for a positive integer $d$ all of whose prime divisors lie in $\{2, 3, 5\}$. Moreover, if $G$ has a composition factor of order 7, then either $E = \mathbb Q(\sqrt{2})$ or $E = \mathbb Q(\sqrt{-3})$. This provides a partial answer to a question of G. Navarro.
Source: arXiv (Cornell University)
Authors: Debón, Sara C., Tent, Joan F.
Institution: Universitat de València
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1021174119, G121809054, G1401168639, G143639328, G1622782223, G1855990336, G2309174360, G252646220, G2585926585, G2660406951, G3518538256, G410571670, G430777504, G451917667, G523076202, G5421974903, G5539308778, G562633673, G5967599077, G6033112984, G6700524545, G7391727506, G8575141037, G8920660035, G897484643, G99296377
OpenAlex ID: W7222516785