What is the Galois Group of $\mathbb{Q}_p(\zeta_p,\sqrt[p]{p})$ where $\zeta_p$ is the primitive p-th root of unity. I know it is a totally ramified extension of degree $p(p-1)$. However, how can I find the Galois group of this extension?
2026-03-26 21:10:21.1774559421
Galois group of finite field extension of p-adic fields
236 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in GALOIS-THEORY
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