PreprintCC BY 4.0arXiv
On a question of Navarro on the field of values of characters of solvable groups
Abstract
In a 2023 survey paper, Gabriel Navarro posed the following problem: Given an irreducible character χ of some solvable group G where χ either is 2-rational or has odd degree, does there exist some g ∈ G such that ℚ(χ(g)) = ℚ(χ)? The answer was recently shown to be no in general by Ulrich Thiel. However, when χ is further assumed to be factorizable as a product of p-special characters, we are able to show that the answer is yes.
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BibTeX
@misc{herbig2026question,
title = {{On a question of Navarro on the field of values of characters of solvable groups}},
author = {Christopher Herbig},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12326},
eprint = {2609.12326},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12326},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a question of Navarro on the field of values of characters of solvable groups
AU - Christopher Herbig
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.12326
UR - https://arxiv.org/abs/2609.12326
AB - In a 2023 survey paper, Gabriel Navarro posed the following problem: Given an irreducible character χ of some solvable group G where χ either is 2-rational or has odd degree, does there exist some g ∈ G such that ℚ(χ(g)) = ℚ(χ)? The answer was recently shown to be no in general by Ulrich Thiel. However, when χ is further assumed to be factorizable as a product of p-special characters, we are able to show that the answer is yes.
ER -