### Abstract

Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the Itô-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup

Original language | English (US) |
---|---|

Pages (from-to) | 1246-1250 |

Number of pages | 5 |

Journal | Bulletin of the London Mathematical Society |

Volume | 44 |

Issue number | 6 |

DOIs | |

State | Published - Dec 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the London Mathematical Society*,

*44*(6), 1246-1250. https://doi.org/10.1112/blms/bds054

**Degrees and p-rational characters.** / Navarro, Gabriel; Tiep, Pham Huu.

Research output: Contribution to journal › Article

*Bulletin of the London Mathematical Society*, vol. 44, no. 6, pp. 1246-1250. https://doi.org/10.1112/blms/bds054

}

TY - JOUR

T1 - Degrees and p-rational characters

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

PY - 2012/12

Y1 - 2012/12

N2 - Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the Itô-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup

AB - Suppose that G is a finite group and that p is a prime number. We prove that if every p-rational irreducible character of G is non-zero on every p-element of G, then G has a normal Sylow p-subgroup. This yields a p-rational refinement of the Itô-Michler theorem: if p does not divide the degree of any irreducible p-rational character of G, then G has a normal Sylow p-subgroup

UR - http://www.scopus.com/inward/record.url?scp=84869456706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869456706&partnerID=8YFLogxK

U2 - 10.1112/blms/bds054

DO - 10.1112/blms/bds054

M3 - Article

AN - SCOPUS:84869456706

VL - 44

SP - 1246

EP - 1250

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 6

ER -