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Let K be a subfield of the complex numbers, and let X be a finite set of complex numbers. If the elements of X are permuted by any automorphism of the complex numbers that fixes K, then the field obtained by adjoining the elements of X to K is a finite, Galois extension of K.

The definitions of Galois extension that I have learned do not seem to yield an easy proof. Any ideas?

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# A Proposition in Galois Theory

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