# character of a finite group

###### Definition.

Let $G$ be a finite group^{}, and let $K$ be a field. A character^{} from $G$ to $K$ is a group homomorphism^{} $\chi \mathrm{:}G\mathrm{\to}{K}^{\mathrm{\times}}$, where ${K}^{\mathrm{\times}}$ is the multiplicative group^{} $K\mathrm{\setminus}\mathrm{\{}{\mathrm{0}}_{K}\mathrm{\}}$.

Example:
The Dirichlet characters^{} are characters from $\mathbb{Z}/m\mathbb{Z}$ to $\u2102$.

Title | character of a finite group |
---|---|

Canonical name | CharacterOfAFiniteGroup |

Date of creation | 2013-03-22 14:10:27 |

Last modified on | 2013-03-22 14:10:27 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 6 |

Author | alozano (2414) |

Entry type | Definition |

Classification | msc 11A25 |

Synonym | character |

Related topic | DirichletCharacter |