5次交错群A_5的10阶子群的一个构造方法  

A Way to Construct Ten-Order Subgroup of A_5

作　　者：孙自行[1] 王雪[1] 

机构地区：[1]阜阳师范学院数学系,安徽阜阳236032

出　　处：《电子科技大学学报》2006年第3期419-422,共4页Journal of University of Electronic Science and Technology of China

基　　金：安徽省自然科学基金资助项目(99047217);安徽省教育厅自然科学基金资助项目(2005KJ399)

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。The maximum order of A5＇s element is 5. By using Lagrange theorem, the could-be order of the element of As＇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 As is fined and therefore 6 10-order subgroup of As are obtained by using the law.

关 键 词：代数编码 形式语言 自动机理论 5次交错群 子群 循环置换 

分 类 号：O152.1[理学—数学]