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- #1

- Mar 10, 2012

- 834

Is it necessary that $[K:F_2]$ is finite and is equal to $n$??

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I have not found this question in a book so I don't know the answer to the above question. I could not construct a counterexample.

If the isomorphism between $F_1$ and $F_2$ can be extended to an automorphism of $K$ (this probably required additional hypothesis) then the result can be proved in the affirmative.