Let K/F be extension field. Let E and L be two intermediate fields. E and L are called conjugate if there is f in Gal(K/E) s.t. f(E)=L .
Show that E and L two conjugate iff Gal(K/E) and Gal(K/L) are conjugate subgroups
For simplicity let A=Gal(K/E) and B=Gal(K/L) . Since E and L are conjugates
then there is f in Gal(K/F) s.t. f(E)=L .
Pleas help on this question.