 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-2/19f/a/solution

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

The kernel is

{g : ρ (g) = I}

and is normal because

ρ (h g h^{- 1}) = ρ (h) ρ (g) ρ (h)^{- 1}

. A one-dimensional representation kills every commutator. Conversely, irreducibles killing

G^{'}

factor through the finite abelian group

G / G^{'}

and are one-dimensional.

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