Let be a finite Galois extension, with Galois group . For set .
(a) Show .
(b) If is a finite field, show that is the map , where .
For (a) show that is fixed for all * which means but because it is Galois.
For (b) since it means where is the Frobenius automorphism, this is enough to prove this result.
*)This is because if is a group with elements then is a permutation.