## $p$-rational characters and self-normalizing Sylow $p$-subgroups

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- by Gabriel Navarro, Pham Huu Tiep and Alexandre Turull PDF
- Represent. Theory
**11**(2007), 84-94 Request permission

## Abstract:

Let $G$ be a finite group, $p$ a prime, and $P$ a Sylow $p$-subgroup of $G$. Several recent refinements of the McKay conjecture suggest that there should exist a bijection between the irreducible characters of $p’$-degree of $G$ and the irreducible characters of $p’$-degree of $\mathbf {N}_G(P)$, which preserves field of values of correspondent characters (over the $p$-adics). This strengthening of the McKay conjecture has several consequences. In this paper we prove one of these consequences: If $p>2$, then $G$ has no non-trivial $p’$-degree $p$-rational irreducible characters if and only if $\mathbf {N}_G(P)=P$.## References

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## Additional Information

**Gabriel Navarro**- Affiliation: Departament d’Àlgebra, Universitat de València, 46100 Burjassot, Spain
- MR Author ID: 129760
- Email: gabriel@uv.es
**Pham Huu Tiep**- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- MR Author ID: 230310
- Email: tiep@math.ufl.edu
**Alexandre Turull**- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
- Email: turull@math.ufl.edu
- Received by editor(s): November 23, 2004
- Published electronically: April 19, 2007
- Additional Notes: The first author was partially supported by the Ministerio de Educación y Ciencia

The second author acknowledges the support of the NSA (grant H98230-04-0066) and the NSF (grant DMS-0600967)

The third author acknowledges the support of the NSA - © Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory
**11**(2007), 84-94 - MSC (2000): Primary 20C15; Secondary 20C33
- DOI: https://doi.org/10.1090/S1088-4165-07-00263-4
- MathSciNet review: 2306612