Find the Galois group of .

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- Apr 5th 2010, 11:53 AMmathman88Galois Group
Find the Galois group of .

- Apr 5th 2010, 02:30 PMchiph588@
I could have this wrong, but here goes:

The splitting field for is , where is a third root of unity.

We then have

Since we can determine all automorphisms based on the roots of and , where is another root of , let's see where that takes us.

Define the automorphisms as follows:

Now note , so .

I'll leave it to you to see why .

So I'm thinking , where is a three-cycle.