摘要
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).
出处
《成都理工大学学报(自然科学版)》
CAS
CSCD
北大核心
2004年第1期100-102,共3页
Journal of Chengdu University of Technology: Science & Technology Edition
基金
成都理工大学信息管理学院自筹基金资助项目(R230246)
关键词
群的阶
群的同构类
整数的独立性
order of groups
isomorphism classes of groups
independence of intergers