For example, consider $[E:F] = 1368$. Since $1368$ is divisible by $36$, is there necessarily some subextension $K/F$ such that $[K:F] = 36$, or is it just possible for one to exist? I have been self-studying abstract algebra for a few months and for some reason, field theory has been incredibly difficult for me to grasp. Thank you so much for any help!
2026-04-07 22:59:42.1775602782
If there is a Galois extension with degree $[E:F] = n$, is there necessarily some subfield $K$ such that $[K:F] = m$ where $m \mid n$?
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