@article{ca1efd75b6274a77b9e02c6a3eeb1887,
title = "Sylow subgroups, exponents, and character values",
abstract = "If G is a finite group, p is a prime, and P is a Sylow p-subgroup of G, we study how the exponent of the abelian group P/P is affected and how it affects the values of the complex characters of G. This is related to Brauer{\textquoteright}s Problem 12. Exactly how this is done is one of the last unsolved consequences of the McKay–Galois conjecture.",
keywords = "Character tables, McKay conjecture, Sylow subgroups",
author = "Gabriel Navarro and Tiep, {Pham Huu}",
note = "Funding Information: The research of the first author is supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2016-76196-P, and FEDER. Funding Information: Received by the editors May 18, 2018, and, in revised form, May 19, 2018, and August 15, 2018. 2010 Mathematics Subject Classification. Primary 20C15; Secondary 20C33, 20D06, 20D20. Key words and phrases. Character tables, Sylow subgroups, McKay conjecture. The research of the first author is supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2016-76196-P, and FEDER. The second author gratefully acknowledges the support of the NSF (grants DMS-1839351 and DMS-1840702). The paper is partially based upon work supported by the NSF under grant DMS-1440140 while the authors were in residence at MSRI (Berkeley, California), during the Spring 2018 semester. We thank the Institute for the hospitality and support. Publisher Copyright: {\textcopyright} 2019 American Mathematical Society.",
year = "2019",
month = sep,
day = "15",
doi = "10.1090/tran7816",
language = "English (US)",
volume = "372",
pages = "4263--4291",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "6",
}