摘要
对任一有限群G和任一正整数d,令G(d)={x∈G|xd=1|}。若G1与G2为有限群,满足|G1(d)|=|G2(d)|,d=1,2,…,则称G1与G2为同阶型群。文中讨论了与Thompson猜想相关的同阶型群的问题,两个有限群阶型相同是否同构的问题,并且对有限群G,定义了G的g函数值g(G),表示与群G的阶型相同的有限群的同构类类数。本文利用4p2阶群的结构完全分类,通过计算得出所有4p2阶群的阶型,对任一4p2阶群M,得出了M的g函数值。特别地,在4p2阶群中找到了一对群,它们的g函数值为2,即阶为4p2的群中存在一对不同构的群,它们阶型相同.这里p为奇素数。
Let G be a finite group and d be a positive integer, let G（d）={x∈G｜x^d=1}. If G1 and G2 are two finite groups, ｜G1（d）｜=｜G2（d）｜,d=1,2,…, then G1 and G2 are groups and their order types are same. In this article we discuss a problem in relation to Thompson supposition, it is that when two finite groups with same order type , they are isomorphic or not, and we define g（G） as the g function value of finite group G ,it represents the number of isomorphic classes that groups with the same order type to G. In this article we obtain the order type of groups with order 4p^2 by computing their constructions, and obtain their g function values. Particularly, we get a pair of groups with order 4p^2 , whose order types are the same and g function values are two, that is, there are two unisomorphic groups with order 4p^2 and their order types are the same. Here p is an odd prime number.
出处
《重庆师范大学学报（自然科学版）》
CAS
2010年第1期53-56,68,共5页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金(No.10771172)
关键词
有限群
阶型
g函数值
finite group
order type
g function value
