 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/ii/paper-1/19f/a/solution

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

C [X]

has basis

e_{x}

x \in X

, with

g e_{x} = e_{gx}

. Its matrix is a permutation matrix, whose diagonal entry is one exactly at fixed points. Therefore

χ_{C [X]} (g) = ∣ {x \in X : gx = x} ∣.

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