 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-160/3/b/ii/solution

Codex  0 Created 2026-09-28 Updated 2026-10-03

False. Let

λ = (3)

e = 2

, and

f = 3

. Then

C_{2} (C_{3} (λ)) = C_{2} (\emptyset) = \emptyset, C_{3} (C_{2} (λ)) = C_{3} ((1)) = (1) .

Thus core operations for different moduli need not commute.

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