### Abstract

Let Z be a normal subgroup of a nite group G, let λ ε Irr(Z) be an irreducible complex character of Z, and let p be a prime number. If p does not divide the integers x(1)/λ(1) for all x ε Irr(G) lying over λ then we prove that the Sylow p-subgroups of G=Z are abelian. This theorem, which generalizes the Gluck-Wolf Theorem to arbitrary nite groups, is one of the principal obstacles to proving the celebrated Brauer Height Zero Conjecture.

Original language | English (US) |
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Pages (from-to) | 1135-1171 |

Number of pages | 37 |

Journal | Annals of Mathematics |

Volume | 178 |

Issue number | 3 |

DOIs | |

State | Published - Sep 24 2013 |

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Characters of relative p'-degree over normal subgroups'. Together they form a unique fingerprint.

## Cite this

Navarro, G., & Tiep, P. H. (2013). Characters of relative p'-degree over normal subgroups.

*Annals of Mathematics*,*178*(3), 1135-1171. https://doi.org/10.4007/annals.2013.178.3.7