## Abstract

The classical Itô-Michler theorem on character degrees of finite groups asserts that if the degree of every complex irreducible character of a finite group G is coprime to a given prime p, then G has a normal Sylow p-subgroup. We propose a new direction to generalize this theorem by introducing an invariant concerning character degrees. We show that if the average degree of linear and even-degree irreducible characters of G is less than 4/3 then G has a normal Sylow 2-subgroup, as well as corresponding analogues for real-valued characters and strongly real characters. These results improve on several earlier results concerning the Itô-Michler theorem.

Original language | English (US) |
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Pages (from-to) | 353-365 |

Number of pages | 13 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 162 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2017 |

## ASJC Scopus subject areas

- General Mathematics