A remark on a conjecture of Navarro and Tiep
Awildo Gutierrez, Yuqiao Huang, Hung Ngoc Nguyen, Duncan Peckham, Yong Yang · Communications in Algebra · 2022
We prove a divisibility property of the fixed field in a cyclotomic field Q(e2iπ/k) of the Frobenius automorphism Gal(Q(e2iπ/k)/Q)∋τ:ξ↦ξp, where p is a prime, k is a positive integer relatively prime to p, and ξ is any kth-root of unity. This implies that, for a finite group G, recent Navarro-Tiep’s conjecture on fields of values of p′-degree irreducible characters of G follows from the celebrated Galois-McKay conjecture under a natural condition on p and the order of G.