摘要
利用计算机,在GAP的环境下进行编程,计算出对称群S10共有1 593个共轭子群类,29594446个子群.其中循环群有42个共轭子群类,可解群有1 418个共轭子群类,幂零群有531个共轭子群类,超可解群有923个共轭子群类,并且通过本文中的表信息可计算出S10中各阶子群的个数及各共轭子群类中所含子群的个数.
By using the GAP, we obtain that S10 contains 1 593 conjugate subgroup classes and 29 594 446 subgroups. The cyclic subgroups consist of 42 conjugate subgroup classes. The solvable subgroups consist of 1 418 conjugate subgroup classes. The nilpotent subgroups have 53I conjugate subgroup classes. The supersolvable subgroups have 923 conjugate subgroup classes. By the table information, we can read off the subgroup number of the specific order and the subgroup number of the particular conjugate subgroup class.
出处
《武汉大学学报（理学版）》
CAS
CSCD
北大核心
2012年第5期451-455,共5页
Journal of Wuhan University:Natural Science Edition
基金
国家自然科学基金资助项目(61074005)
辽宁省教育厅基金资助项目(2008516)
关键词
对称群
共轭子群类
极大子群
算法
symmetric group
conjugate subgroup class
maximal subgroup
algorithm
