Michael Artin's algebra:
9.8 Porposition. let $f$ be a polynomial over $F$ whose Galois group $G$ is a simple nonabelian group. Let $F'$ be a Galois extension of $F$, with abelian Galois group. Let $K'$ be a splitting field of $f$ over $F'$. Then the Galois group $G(K'/F')$ is isomorphic to G
in my understanding , Galois is always linked with extension field. but here the Galois group is simply attached to a function definition , what does this mean ?
it is just the definition that matters.
plus can someone elaborate on the proval ?