### 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) |
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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 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Navarro, G., & Tiep, P. H. (2012). Degrees and p-rational characters.

*Bulletin of the London Mathematical Society*,*44*(6), 1246-1250. https://doi.org/10.1112/blms/bds054