置换群及其在对称变换和现实生活中的应用

Discussion on permutation groups and their applications in symmetric transformation and real life

研究了置换群的性质,对置换群中元素的性质、置换群的对称性及置换群的子群的求法等作了一个全面系统的整合,对一些性质给出了更通俗易懂的证法.最后根据性质讨论了置换群在对称变换和现实生活中的应用。

This paper studies the properties of permutation group,and makes a comprehensive and systematic integration of the properties of the elements in permutation group,the symmetry of permutation group and the method of finding subgroups of permutation group,and gives more easily understood proofs for some properties.Finally,the applications of permutation groups in symmetric transformation and real life are discussed.