# fixed field

Let $K/F$ be a field extension with Galois group^{} $G=\mathrm{Gal}(K/F)$, and let $H$ be a subgroup^{} of $G$. The fixed field of $H$ in $K$ is the set

$${K}^{H}:=\{x\in K\mid \sigma (x)=x\text{for all}\sigma \in H\}.$$ |

The set ${K}^{H}$ is always a field, and $F\subset {K}^{H}\subset K$.

Title | fixed field |
---|---|

Canonical name | FixedField |

Date of creation | 2013-03-22 12:08:24 |

Last modified on | 2013-03-22 12:08:24 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 6 |

Author | djao (24) |

Entry type | Definition |

Classification | msc 12F10 |