Real ordinary characters and real Brauer characters
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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 $1$.References
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Additional Information
- Pham Huu Tiep
- Affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721
- MR Author ID: 230310
- Email: tiep@math.arizona.edu
- 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) - © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3280044
Dedicated: Dedicated to the memory of Professor D. Chillag