### Abstract

We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then O<sup>p'</sup>(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.

Original language | English (US) |
---|---|

Pages (from-to) | 1273-1312 |

Number of pages | 40 |

Journal | Transactions of the American Mathematical Society |

Volume | 367 |

Issue number | 2 |

State | Published - 2015 |

### Fingerprint

### Keywords

- Frobenius-Schur indicator
- Real-valued Brauer characters
- Real-valued ordinary characters

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*367*(2), 1273-1312.

**Real ordinary characters and real brauer characters.** / Tiep, Pham Huu.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 367, no. 2, pp. 1273-1312.

}

TY - JOUR

T1 - Real ordinary characters and real brauer characters

AU - Tiep, Pham Huu

PY - 2015

Y1 - 2015

N2 - We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then Op'(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.

AB - We prove that if G is a finite group and p is a prime such that the degree of every real-valued irreducible complex, respectively real-valued irreducible p-Brauer character, of G is coprime to p, then Op'(G) is solvable. This result is a generalization of the celebrated Ito-Michler theorem for real ordinary characters, respectively real Brauer characters, with Frobenius-Schur indicator 1.

KW - Frobenius-Schur indicator

KW - Real-valued Brauer characters

KW - Real-valued ordinary characters

UR - http://www.scopus.com/inward/record.url?scp=84928241070&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928241070&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84928241070

VL - 367

SP - 1273

EP - 1312

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -