Illustrate Burnside's Lemma for the action of A4 on the vertices of a regular tetrahedron.
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In this case, A4 is the group of even permutations of four elements. Let's label the vertices of the regular tetrahedron as 1, 2, 3, and 4. - The identity permutation (1 2 3 4) fixes all four vertices, so it has 4 fixed points. - The 3-cycles (1 2 3) and (1 3 Show more…
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