### Abstract

Let G be a finite group and let p be an odd prime. Under certain conditions on the p-parts of the degrees of its irreducible p-Brauer characters, we prove the solvability of G. As a consequence, we answer a question proposed by B. Huppert in 1991: If G has exactly two distinct irreducible p-Brauer character degrees, then is G solvable? We also determine the structure of non-solvable groups with exactly two irreducible 2-Brauer character degrees.

Original language | English (US) |
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Pages (from-to) | 426-438 |

Number of pages | 13 |

Journal | Journal of Algebra |

Volume | 403 |

DOIs | |

State | Published - Feb 1 2014 |

### Keywords

- Brauer characters
- Solvable groups

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Navarro, G., Tiep, P. H., & Tong-Viet, H. P. (2014). P-Parts of Brauer character degrees.

*Journal of Algebra*,*403*, 426-438. https://doi.org/10.1016/j.jalgebra.2014.01.022