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Transactions of the American Mathematical Society

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

 
 

 

Sylow subgroups, exponents, and character values


Authors: Gabriel Navarro and Pham Huu Tiep
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 20C15; Secondary 20C33, 20D06, 20D20
DOI: https://doi.org/10.1090/tran/7816
Published electronically: April 4, 2019
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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'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
Email: gabriel@uv.es

Pham Huu Tiep
Affiliation: Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854
Email: tiep@math.rutgers.edu

DOI: https://doi.org/10.1090/tran/7816
Keywords: Character tables, Sylow subgroups, McKay conjecture
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.
Article copyright: © Copyright 2019 American Mathematical Society