Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?
I am inclined to say 4 but I cannot prove it.
2026-04-04 12:00:16.1775304016
Take a galois group $Gal(K/\mathbb{Q})$ isomorphic to $C_{16}$. How many subfields $L$ exist such that $[K:L] = 4$?
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Hint
This is exactly Galois theorem : you have a one to one correspondance between the sub-fields of degree 4 of $L$ and the subgroups of $C_{16}$ with 4 elements.