中文摘要：

对任一有限群G和任一正整数d，令G（d）={x∈G｜x^d=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尊的问题，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4p^2阶群的结构完全分类，通过计算得出所有和。阶群的阶型，对任一4p^2阶群M，得出了M的g函数值。特别地，在4p^2阶群中找到了一对群，它们的g函数值为2．即阶为4p^2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。

英文摘要：

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.