How many intermediate fields?

by Marcos G Neil   Last Updated August 14, 2019 09:20 AM - source

Let $$F ⊂ L$$ a extension of fields of degree 4. Prove that there are no more than 3 fields proper intermediate subfields $$K$$; namely, such that $$F ⊂ K ⊂ L$$

Using the degree of the field extension, I only know that $$K$$ is a field extension of $$F$$ of degree 2. This question is quite more specific than related questions on stack already. So how can we solve this?

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