Cyclotomic character fields and sets of primes

Eugenio Giannelli; J. Miquel Martínez; Carolina Vallejo

Cyclotomic character fields and sets of primes

Representation Theory 2026-07-18 v1

Authors: Eugenio Giannelli , J. Miquel Martínez , Carolina Vallejo

Abstract

Let $\pi=\{ 2, q \}$ where $q$ is an odd prime. Let $G$ be a finite group of order divisible by a prime $p \in \pi$ . We show that the principal $p$ -block of $G$ contains a nontrivial irreducible character of degree not divisible by $2$ nor $q$ and with field of values contained in the $q$ th cyclotomic extension. This statement simultaneously provides a principal block version of results of Navarro--Tiep and Giannelli--Hung--Schaeffer Fry--Vallejo.

Keywords

character fields principal blocks irreducible characters cyclotomic extensions

Cite

@article{arxiv.2607.16732,
  title  = {Cyclotomic character fields and sets of primes},
  author = {Eugenio Giannelli and J. Miquel Martínez and Carolina Vallejo},
  journal= {arXiv preprint arXiv:2607.16732},
  year   = {2026}
}