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In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G. The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2,..., n} then Sym(M) is usually denoted by Sn, and may ... Wikipedia