置换群
数学上，一个置换群是一个群G，其元素是一个给定集M的置换，而其群作用是G中的置换（可以看作是从M到自身的双射）的复合；其关系经常写作(G,M)。注意所有置换的群是对称群；置换群通常是指对称群的一个子群。n个元素的置换群记为Sn；若M是任意有限或无限集合，则所有M的置换组成的对称群通常写作Sym(M)。
置换群到被置换的元素的应用称为群作用；它在对称性和组合论以及数学的其他很多分支中有应用。
Permutation group
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Permutation group 置换群
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 (which are thought of as bijective functions from the set M to itself). 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), the symmetric group on n letters is usually denoted by Sn.
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