 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2011/ii/paper-3/18h/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-14

The cyclotomic Galois group theorem states

Gal (Q (μ_{n}) / Q) ≅ (Z / n Z)^{\times}, σ_{b} (ζ_{n}) = ζ_{n}^{b},

for

b

n

, with

[Q (μ_{n}) : Q] = φ (n)

, where

φ

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