具有6个同构类的群的无平方因子的阶

Square-free order of the group with six isomorphism classes

对群计数公式的研究是有限群理论中有着重大意义的问题,设f(n)是n阶群的同构类数目,对于给定的整数k,去寻找满足f(n)=k的整数n,叫做求方程f(n)=k的解。作者利用Balass公式对具有6个同构类的群的无平方因子阶进行分析讨论,得到了方程f(n)=6的所有无平方因子解。

One of the important problems in the theory of finite groups is the enumeration formulae for the number of finite groups. If f(n) is the number of isomorphism classes of groups with n order, for a given integer k, then to find the integer n satisfied with f(n)=k is said to gain a solution of the equation f(n)=k. In this paper, the square-free order is analyzed and solutions for f(n)=6 are listed by using Balass (equation).