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

Pages (from-to) | 426-438 |

Number of pages | 13 |

Journal | Journal of Algebra |

Volume | 403 |

DOIs | |

State | Published - Feb 1 2014 |

### Fingerprint

### Keywords

- Brauer characters
- Solvable groups

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Journal of Algebra*,

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

**P-Parts of Brauer character degrees.** / Navarro, Gabriel; Tiep, Pham Huu; Tong-Viet, Hung P.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - P-Parts of Brauer character degrees

AU - Navarro, Gabriel

AU - Tiep, Pham Huu

AU - Tong-Viet, Hung P.

PY - 2014/2/1

Y1 - 2014/2/1

N2 - 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.

AB - 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.

KW - Brauer characters

KW - Solvable groups

UR - http://www.scopus.com/inward/record.url?scp=84893476385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893476385&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2014.01.022

DO - 10.1016/j.jalgebra.2014.01.022

M3 - Article

VL - 403

SP - 426

EP - 438

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -