摘要
文章讨论了与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3p^2阶群的结构完全分类,通过计算得出所有3p^2阶群的阶型,对任一3p^2阶群M,得出了M的g函数值。特别地,在3p^2阶群中找到了g函数值为2的群,即阶为3p^2的群中存在一对不同构的群,但它们阶型相同。这里p为奇素数。
A problem in relation to Thompson supposition is discussed, it is that when two finite groups with same order type, Wether they are isomorphic or not. 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 and g function values with order 3p^2 by computing their constructions. Particularly, we get groups with order 3p^2 , whose order types are same and the same g function value is 2, that is, there are two unisomorphic groups with order 3p^2 , their order types are same. Here p is an odd prime number.
出处
《四川理工学院学报（自然科学版）》
CAS
2009年第6期42-44,共3页
Journal of Sichuan University of Science & Engineering(Natural Science Edition)
关键词
有限群
阶型
g函数值
finite group
order type
g function value
