Let L/K be a Galois extension with Galois group isomorphic to A4. Let g(x) ϵ K [x] be an irreducible polynomial that is degree 3 that splits in L. Show that the Galois group of
g(x) over K is cyclic.
The Attempt at a Solution
I know, Galois means normal and separable.
Irrdeducible poly of degree 3 that splits in L means it splits into linear factors.
I am thinking Galois correspondence might come in handy, but not sure how...any ideas?
I'm not sure what information Cyclic gives.