### Abstract

We provide an alternative constructive proof of the classical Brauer theorem for finite groups based on the well-known description of the complex irreducible representations of the symmetric groups Sn. The theorem is first proved for Sn and then for general G by embedding in Sn and applying the Mackey subgroup theorem.

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

Pages (from-to) | 31-53 |

Number of pages | 23 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 57 |

Issue number | 1 |

DOIs | |

State | Published - 2014 |

### Fingerprint

### Keywords

- Brauer theorem
- induced characters
- long cycles
- symmetric groups
- Young diagrams

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the Edinburgh Mathematical Society*,

*57*(1), 31-53. https://doi.org/10.1017/S0013091513000904

**A constructive proof of Brauer's theorem on induced characters in the group Ring[G].** / Bogomolov, Fedor; Greenleaf, Frederick P.

Research output: Contribution to journal › Article

*Proceedings of the Edinburgh Mathematical Society*, vol. 57, no. 1, pp. 31-53. https://doi.org/10.1017/S0013091513000904

}

TY - JOUR

T1 - A constructive proof of Brauer's theorem on induced characters in the group Ring[G]

AU - Bogomolov, Fedor

AU - Greenleaf, Frederick P.

PY - 2014

Y1 - 2014

N2 - We provide an alternative constructive proof of the classical Brauer theorem for finite groups based on the well-known description of the complex irreducible representations of the symmetric groups Sn. The theorem is first proved for Sn and then for general G by embedding in Sn and applying the Mackey subgroup theorem.

AB - We provide an alternative constructive proof of the classical Brauer theorem for finite groups based on the well-known description of the complex irreducible representations of the symmetric groups Sn. The theorem is first proved for Sn and then for general G by embedding in Sn and applying the Mackey subgroup theorem.

KW - Brauer theorem

KW - induced characters

KW - long cycles

KW - symmetric groups

KW - Young diagrams

UR - http://www.scopus.com/inward/record.url?scp=84897026544&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897026544&partnerID=8YFLogxK

U2 - 10.1017/S0013091513000904

DO - 10.1017/S0013091513000904

M3 - Article

AN - SCOPUS:84897026544

VL - 57

SP - 31

EP - 53

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 1

ER -