5次交错群A5的10阶子群的一个构造方法
A Way to Construct Ten-Order Subgroup of A5
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摘要: A5的元最大阶数是5,使用有限群的Lagrange定理,A5的10阶子群元的阶只可能是2,5。但由于拉格朗日定理的逆不成立,因此是否存在A5的10阶子群仍是问题。该文通过对5-循环置换各次方幂的计算及其研究,找到A5的10阶子群元的构成规律,并使用构造性方法给出了5次交错群A5的6个10阶子群。Abstract: The maximum order of A5's element is 5. By using Lagrange theorem, the could-be order of the element of A5's subgroup are 2 and 5, but in general the inverse of the Lagrange theorem is not hold, whether the ten-order subgroup of A5 exist is still a problem to discuss. Based on the researching and calculation on the power of 5-cyclic permutation, the forming law of the 10 order subgroup of A5 is fined and therefore 6 10-order subgroup of A5 are obtained by using the law.