 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/19h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The commutator subgroup equals the centre, so

G / [G, G] ≅ F_{p}^{2} .

Fix

ω = e^{2 πi / p}

χ_{a, b} (x, y, z) = ω^{a x + b y}, a, b \in F_{p},

and these

p^{2}

distinct characters exhaust the one-dimensional representations.

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