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Real ordinary characters and real Brauer characters


Author: Pham Huu Tiep
Journal: Trans. Amer. Math. Soc. 367 (2015), 1273-1312
MSC (2010): Primary 20C15, 20C20, 20C33
DOI: https://doi.org/10.1090/S0002-9947-2014-06148-5
Published electronically: October 10, 2014
MathSciNet review: 3280044
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Abstract: We prove that if $ G$ is a finite group and $ p$ is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible $ p$-Brauer character, of $ G$ is coprime to $ p$, then $ \mathbf {O}^{p'}(G)$ is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator $ 1$.


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Additional Information

Pham Huu Tiep
Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Email: tiep@math.arizona.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-06148-5
Keywords: Real-valued ordinary characters, real-valued Brauer characters, Frobenius-Schur indicator
Received by editor(s): December 23, 2012
Received by editor(s) in revised form: April 9, 2013
Published electronically: October 10, 2014
Additional Notes: The author is grateful to Robert M. Guralnick and Gabriel Navarro for helpful comments on the topic of the paper. He also thanks the referee for helpful comments that greatly improved the exposition of the paper.
The author gratefully acknowledges the support of the NSF (grants DMS-0901241 and DMS-1201374)
Dedicated: Dedicated to the memory of Professor D. Chillag
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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