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讨论了正形置换的构造和性质,并分析了正形置换的幂次是否仍是正形置换.对于线性正形置换,根据矩阵标准型的性质,只要整数i不能被这个正形置换对应矩阵的极小多项式的各个根的阶整除,则这个线性正形置换的i次幂仍是线性正形置换.对于非线性正形置换,给出了有用的结果.
We discuss the construction and properties of orthomorphic permutations and analyze whether the power of orthomorphic permutations is still orthomorphic permutations.For linear orthomorphic permutations, according to the nature of the standard matrix, as long as the integer i can not be replaced by the orthomorphic matrices The order of divisors of the roots of the minimal polynomial is then linearly orthomorphic for the i-th power of this linear orthomorphic permutation. For non-linear orthomorphic permutations, useful results are given.