[alogo] The alternating group A4


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A tree representing the 24 elements of the symmetric group S4 of four elements. The permutations denoted by ai are the elements of the alternating group A4. Below is given the multiplication table of A4, the numbers representing the indices of ai. A remarkable property of this table is that for two elements on a row, which are symmetric with respect to the middle of the row, the sum of their indices is 13. Why?

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