1. A remark on a conjecture of Navarro and Tiep.
- Author
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Gutierrez, Awildo, Huang, Yuqiao, Ngoc Hung, Nguyen, Peckham, Duncan, and Yang, Yong
- Subjects
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CYCLOTOMIC fields , *LOGICAL prediction , *FINITE groups , *DIVISIBILITY groups , *SOLVABLE groups - Abstract
We prove a divisibility property of the fixed field in a cyclotomic field Q (e 2 i π / k) of the Frobenius automorphism Gal (Q (e 2 i π / k) / Q) ∋ τ : ξ ↦ ξ p , where p is a prime, k is a positive integer relatively prime to p, and ξ is any k th -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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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