 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ib/paper-1/9e/a/i/solution

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

Since

∣ S_{3} ∣ = 6

, its Sylow

2

-subgroups have order two and its Sylow

3

-subgroups have order three. They are

⟨(12)⟩, ⟨(13)⟩, ⟨(23)⟩

and

A_{3} = ⟨(123)⟩,

respectively. The latter is the unique Sylow

3

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