SOLUTION: Give an example of a group of size four, acting on a set of size four. And describe its orbits and stabilizers.

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Question 865859: Give an example of a group of size four, acting on a set of size four. And describe its orbits and stabilizers.
Answer by richard1234(7193) About Me  (Show Source):
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For example, let (that is, the elements of G are 1, x, x^2, x^3 with x^4 = 1), and suppose G acts on . Then, for ,




It follows that for all , and .

This satisfies the orbit-stabilizer theorem for .