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Finite groups with odd Sylow normalizers

Authors: Robert M. Guralnick, Gabriel Navarro and Pham Huu Tiep
Journal: Proc. Amer. Math. Soc. 144 (2016), 5129-5139
MSC (2010): Primary 20D06; Secondary 20D20
Published electronically: June 10, 2016
MathSciNet review: 3556259
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Abstract: We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these groups at these primes.

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Robert M. Guralnick
Affiliation: Department of Mathematics, University of Southern California, 3620 S. Vermont Avenue, Los Angeles, California 90089

Gabriel Navarro
Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, València, Spain

Pham Huu Tiep
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Keywords: McKay conjecture, Alperin's weight conjecture, Sylow normalizers
Received by editor(s): February 24, 2016
Published electronically: June 10, 2016
Additional Notes: The first author gratefully acknowledges the support of the NSF grant DMS-1302886.
The research of the second author was supported by the Prometeo/Generalitat Valenciana, Proyectos MTM2013-40464-P. He would like to express his gratitude to the Mathematics Department of the University of Southern California where part of the present work was completed for its warm hospitality.
The third author was partially supported by the NSF grant DMS-1201374 and the Simons Foundation Fellowship 305247. Part of this work was done while the third author visited the Institute for Advanced Study (Princeton, NJ). It is a pleasure to thank Peter Sarnak and the Institute for their generous hospitality and a stimulating environment.
The authors are grateful to Gunter Malle for helpful comments on the paper, and to the referee for a careful reading of the paper.
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society

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