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arXiv · 2607.16732

Cyclotomic character fields and sets of primes

Eugenio Giannelli·J. Miquel Martínez·Carolina Vallejo
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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.

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BibTeXRIS

Eugenio Giannelli, J. Miquel Martínez, Carolina Vallejo. 2026-07-18. Cyclotomic character fields and sets of primes. https://arxiv.org/abs/2607.16732

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