Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 3 / 5D / a / i

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- Solution i

Solution

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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