 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-3/1d/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

False. Take

G = C_{2} \times C_{2}

and let

N

be either factor. Then

N ≅ C_{2}

and

G / N ≅ C_{2}

, but

G

is not cyclic and hence is not

C_{4}

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