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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Updated January 02, 2019 17:20 PM