 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-3/5d/ii/solution

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

No. In any group choose a nonidentity

x

and put

y = x^{- 1}

. They commute, but

x y = e

has order one rather than

o (x) o (y)

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