### 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) |
---|---|

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 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*361*(12), 6521-6547. https://doi.org/10.1090/S0002-9947-09-04718-7

**Groups with just one character degree divisible by a given prime.** / Isaacs, I. M.; Moretó, Alexander; Navarro, Gabriel; Tiep, Pham Huu.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 361, no. 12, pp. 6521-6547. https://doi.org/10.1090/S0002-9947-09-04718-7

}

TY - JOUR

T1 - Groups with just one character degree divisible by a given prime

AU - Isaacs, I. M.

AU - Moretó, Alexander

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

PY - 2009/12

Y1 - 2009/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77950633644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950633644&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-09-04718-7

DO - 10.1090/S0002-9947-09-04718-7

M3 - Article

AN - SCOPUS:77950633644

VL - 361

SP - 6521

EP - 6547

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 12

ER -