### Abstract

The Ito-Michler theorem asserts that if no irreducible character of a finite group G has degree divisible by some given prime p, then a Sylow p-subgroup of G is both normal and abelian. In this paper we relax the hypothesis, and we assume that there is at exactly one multiple of p that occurs as the degree of an irreducible character of G. We show that in this situation, a Sylow p-subgroup of G is almost normal in G, and it is almost abelian.

Original language | English (US) |
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Pages (from-to) | 6521-6547 |

Number of pages | 27 |

Journal | Transactions of the American Mathematical Society |

Volume | 361 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2009 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Isaacs, I. M., Moretó, A., Navarro, G., & Tiep, P. H. (2009). Groups with just one character degree divisible by a given prime.

*Transactions of the American Mathematical Society*,*361*(12), 6521-6547. https://doi.org/10.1090/S0002-9947-09-04718-7