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Symmetric group:S3 - Groupprops

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We portray elements as permutations on the set using the cycle decomposition. The row element is multiplied on the left and the column element on the right, with the assumption of functions written on the left. This means that the column element is applied first and the row element is applied next. If we used the opposite convention (i.e., functions written on the right), the row element is to be multiplied on the right and the column element on the left. Here is the multiplication table where we use the one-line notation for permutations, where, as in the previous multiplication table, the column permutation is applied first and then the row permutation. Thus, with the left action convention, the row element is multiplied on the left and the column element on the right: The symmetric group on three elements is part of some important families: Further information: Element structure of symmetric group:S3 As for any symmetric group, cycle type determines conjugacy class. The cycle types

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