 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-3/5d/a/i/solution

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

The orbit and stabiliser are

G x = {gx : g \in G}, Stab_{G} (x) = {g \in G : gx = x} .

Such an action can be faithful: the natural action of

S_{3}

on three points is faithful, although every point stabiliser has order two.

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