Let be a polynomial over a field , and let be its splitting field. If is a radical extension of , then the Galois group is a solvable group.
Conversely, if the Galois group is a solvable group, then is a radical extension of provided that the characteristic of is either 0 or greater than .
![$ f \in F[x]$](http://images.planetmath.org:8080/cache/objects/1338/l2h/img1.png "$ f \in F[x]$"){kind=small}
