| Lagrange定理的逆问题的一些探讨 |
| |
| 引用本文： | 王珊珊.Lagrange定理的逆问题的一些探讨[J].顺德职业技术学院学报,2012,10(3):21-23,42. |
| |
| 作者姓名： | 王珊珊 |
| |
| 作者单位： | 华南师范大学数学科学学院数学与应用数学系,广东广州,510631 |
| |
| 摘 要： | 总结了有限交换群和一般有限群情形下Lagrange定理的逆问题的探讨和结论,并分别给出了例子。特别地,对于有限非交换群情形下,Lagrange定理的逆问题一般有否定答案的情况给出例子——24阶置换群S4的所有偶置换的集形成的4次交代群不存在6阶子群来加以说明。
|
| 关 键 词： | Lagrange定理 逆问题 群论 |
Discussion on the Converse Problem of Lagrange's Theorem |
| |
| Authors: | WANG Shan-shan |
| |
| Institution: | WANG Shan-shan (School of Mathematical Sciences,South China Normal University,Guangzhou Guangdong 510631,China) |
| |
| Abstract: | This paper aims to summarize the discussion on the converse problem of Lagrange’s Theorem when G is a finite group or a general group,and gives examples for each of them.Besides,an example given in this paper shows that no subgroup of order 6 of A4 is formed by the set of all the even permutation of S4 and explains that the converse problem is Lagrange’s Theorem is wrong. |
| |
| Keywords: | Lagrange’s Theorem converse problem group theory |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
