@article{92a73f2a7c534836b050eb8c3f021a99,
title = "On real and rational characters in blocks",
abstract = "The principal $p$-block of a finite group $G$ contains only one real-valued irreducible ordinary character exactly when $G/{{\bf O}-{p'}(G)}$ has odd order. For $p \ne 3$, the same happens with rational-valued characters. We also prove an analogue for $p$-Brauer characters with $p \geq 3$.",
keywords = "20C15, 20C20",
author = "Gabriel Navarro and Robinson, {Geoffrey R.} and Tiep, {Pham Huu}",
note = "Funding Information: This work was partially supported by the Spanish Ministerio de Educaci{\'o}n y Ciencia Proyecto MTM2016-76196-P, Feder funds, and Prometeo II/Generalitat Valenciana to G.N. and National Science Foundation (grants DMS-1201374 and DMS-1665014) and a Clay Senior Scholarship to P.H.T. Funding Information: The authors are grateful to Thomas Breuer for providing them with a proof of Theorem 4.5 for sporadic simple groups, and to Meinolf Geck, Gerhard Hiss, and Jay Taylor for helpful discussions. They are also grateful to the referees for careful reading and helpful comments on the article. Part of the article was written while G.N. visited the Department of Mathematics, University of Arizona. It is a pleasure to thank the University of Arizona and the NSF for financial support, kind hospitality, and stimulating environment. Publisher Copyright: {\textcopyright} 2017 The Author(s) 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permission@oup.com.",
year = "2019",
month = apr,
doi = "10.1093/imrn/rnx170",
language = "English (US)",
volume = "2019",
pages = "1955--1973",
journal = "International Mathematics Research Notices",
issn = "1073-7928",
publisher = "Oxford University Press",
number = "7",
}