作 者: ;
机构地区: 华南师范大学数学科学学院
出 处: 《顺德职业技术学院学报》 2012年第3期21-23,42,共4页
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。 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 $4 and explains that the converse problem is Lagrange's Theorem is wrong.