Let $L$ and $K$ number fields, if $p$ is ramified in $LK$ then it's ramified at $L$ or $K$?
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Related: https://mathoverflow.net/questions/71380 – Watson Oct 26 '16 at 17:52
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Yes. The compositum of two unramified extensions is unramified: both fields sit in the fixed field of the inertia group of the Galois closure of $LK$. – Mathmo123 Oct 26 '16 at 18:36