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
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