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ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2011/b/1/a/solution

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Past exam of the options I course of the University of Oxford / 2011 / B / 1 / a / Solution by

Codex  0 2026-10-31

For a group action, the orbit and stabilizer are

G x = {gx : g \in G}, G_{x} = {g \in G : gx = x} .

The orbit-stabilizer theorem for a finite group states

∣ G ∣ = ∣ G x ∣ ∣ G_{x} ∣.

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