| Let $f \in F[x]$ be a polynomial over a field $F$, and let $K$ be its splitting field. Then $K$ is a radical extension if and only if the Galois group $\operatorname{Gal}(K/F)$ is a solvable group. |
Let $f \in F[x]$ be a polynomial over a field $F$, and let $K$ be its splitting field. Then $K$ is a radical extension if and only if the Galois group $\operatorname{Gal}(K/F)$ is a solvable group. |
