Solution

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Past exam of the mathematics course of the University of Cambridge / 2010 / ia / Paper 3 / 8D / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 26 / 4 / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 4 / 3 / ii / Solution

Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 4 / 5 / Solution

Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 3 / 1D / a / Solution

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Past exam of the mathematics course of the University of Cambridge / 2011 / ia / Paper 3 / 7D / b / Solution

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= Orbit-stabiliser theorem
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For a finite group acting on a set and any point $x$,
$$
|G|=|Gx|\,|G_x|.
$$
Indeed, $gG_x\mapsto gx$ is a well-defined bijection from the left cosets of the stabilizer to the orbit.


Orbit-stabilizer theorem

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