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# Galois conjugate

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## Comments

## Galois conjugates?

If L is not a Galois extension of K, are the Galois conjugates of x really only the images of x that lie in L? I thought they would include the entire orbit of x under the Galois group.

## Re: Galois conjugates?

In the text I have specified that L is a separable closure of K, so L/K is guaranteed to be Galois.