Imperial College London
Professor Martin Liebeck

ProfessorMartinLiebeck

Faculty of Natural Sciences, Department of Mathematics

Head of Pure Mathematics Section/Prof of Pure Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8490m.liebeck Website

 
 
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Location

 

665Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Isaacs:2019:10.1016/j.aim.2019.106757,
author = {Isaacs, IM and Liebeck, M and Navarro, G and Tiep, PH},
doi = {10.1016/j.aim.2019.106757},
journal = {Advances in Mathematics},
title = {Fields of values of odd-degree irreducible characters},
url = {http://dx.doi.org/10.1016/j.aim.2019.106757},
volume = {354},
year = {2019}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - In this paper we clarify the quadratic irrationalities that can be admittedby an odd-degree complex irreducible character χ of an arbitrary finite group. WriteQ(χ) to denote the field generated over the rational numbers by the values of χ, andlet d > 1 be a square-free integer. We prove that if Q(χ) = Q(√d) then d ≡ 1 (mod4) and if Q(χ) = Q(√−d), then d ≡ 3 (mod 4). This follows from the main result ofthis paper: either i ∈ Q(χ) or Q(χ) ⊆ Q(exp(2πi/m)) for some odd integer m ≥ 1.
AU  - Isaacs,IM
AU  - Liebeck,M
AU  - Navarro,G
AU  - Tiep,PH
DO  - 10.1016/j.aim.2019.106757
PY  - 2019///
SN  - 0001-8708
TI  - Fields of values of odd-degree irreducible characters
T2  - Advances in Mathematics
UR  - http://dx.doi.org/10.1016/j.aim.2019.106757
UR  - http://hdl.handle.net/10044/1/72229
VL  - 354
ER  -
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