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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Sylow subgroups, exponents, and character values
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by Gabriel Navarro and Pham Huu Tiep PDF
Trans. Amer. Math. Soc. 372 (2019), 4263-4291 Request permission


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’s Problem $12$. Exactly how this is done is one of the last unsolved consequences of the McKay–Galois conjecture.
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Additional Information
  • Gabriel Navarro
  • Affiliation: Departament de Matemàtiques, Universitat de València, 46100 Burjassot, València, Spain
  • MR Author ID: 129760
  • Email:
  • Pham Huu Tiep
  • Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
  • MR Author ID: 230310
  • Email:
  • Received by editor(s): May 18, 2018
  • Received by editor(s) in revised form: May 19, 2018, and August 15, 2018
  • Published electronically: April 4, 2019
  • Additional Notes: 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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 4263-4291
  • MSC (2010): Primary 20C15; Secondary 20C33, 20D06, 20D20
  • DOI:
  • MathSciNet review: 4009430