 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ib/paper-1/8f/b/solution

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

False. At eigenvalue

2

J_{2} (2)

1

, the blocks have total size five and largest size two, so there are only two possible partitions,

2 + 2 + 1 or 2 + 1 + 1 + 1.

Hence there are exactly two conjugacy classes satisfying the given polynomial data, represented by

J_{2} (2) \oplus J_{2} (1) \oplus J_{2} (1) \oplus J_{1} (1)

and

J_{2} (2) \oplus J_{2} (1) \oplus J_{1} (1) \oplus J_{1} (1) \oplus J_{1} (1) .

There cannot be three mutually non-conjugate examples.

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