# Shafarevich’s theorem

###### Theorem (Shafarevich’s Theorem).

Every finite solvable group^{} occurs as a Galois group^{} of a finite extension^{} of $\mathrm{Q}$.

One can find a proof in [S-W].

## References

- S-W Alexander Schmidt and Kay Wingberg, http://www.math.uiuc.edu/Algebraic-Number-Theory/0136/Shafarevich’s Theorem on Solvable Groups as Galois Groups.

Title | Shafarevich’s theorem |
---|---|

Canonical name | ShafarevichsTheorem |

Date of creation | 2013-03-22 15:01:17 |

Last modified on | 2013-03-22 15:01:17 |

Owner | alozano (2414) |

Last modified by | alozano (2414) |

Numerical id | 8 |

Author | alozano (2414) |

Entry type | Theorem |

Classification | msc 11R32 |

Related topic | InverseGaloisProblem |

Related topic | Solvable |