1. The problem statement, all variables and given/known data 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. 2. Relevant equations 3. 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. ie. g(x)=(x-a1)*(x-a2)*(x-a3) I am thinking Galois correspondence might come in handy, but not sure how...any ideas? I'm not sure what information Cyclic gives.