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 .

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- May 29th 2008, 05:10 PMheathrowjohnnyGalois Extension
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 . - May 29th 2008, 05:21 PMThePerfectHacker
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.