# Galois criterion for solvability of a polynomial by radicals

Let $f\in F[x]$ be a polynomial^{} over a field $F$, and let $K$ be its splitting field^{}. If $K$ is a radical extension of $F$, then the Galois group^{} $\mathrm{Gal}(K/F)$ is a solvable group^{}.

Conversely, if the Galois group $\mathrm{Gal}(K/F)$ is a solvable group, then $K$ is a radical extension of $F$ provided that the characteristic^{} of $K$ is either $0$ or greater than $\mathrm{deg}(f)$.

Title | Galois criterion for solvability of a polynomial by radicals^{} |
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Canonical name | GaloisCriterionForSolvabilityOfAPolynomialByRadicals |

Date of creation | 2013-03-22 12:08:58 |

Last modified on | 2013-03-22 12:08:58 |

Owner | djao (24) |

Last modified by | djao (24) |

Numerical id | 7 |

Author | djao (24) |

Entry type | Theorem |

Classification | msc 11R32 |