| 计算机代数在有限群同构类计数中的设计与应用 |
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| 引用本文： | 邱燕红,田宝单.计算机代数在有限群同构类计数中的设计与应用[J].四川理工学院学报(自然科学版),2008,21(4). |
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| 作者姓名： | 邱燕红 田宝单 |
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| 作者单位： | 西南科技大学理学院,四川,绵阳,621010 |
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| 基金项目： | 西南科技大学青年科技基金 |
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| 摘 要： | 文献1]论证n阶群同构类的个数在1000以内的存在性。文章给出群同构类Balass计数公式运算的算法,用计算机代数语言Matlab加以实现,进而将群同构类的个数推广到3000。即设f(n)为n阶群同构类的个数,证明方程f(n)=k,(1≤k≤3000)解的存在性。
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| 关 键 词： | 有限群 群的同构类的个数 Balass公式 |
Realization on the Computer Algebra about Enumeration Formulas for the Number of Isomorphism Classes of Finite Groups |
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| QIU Yan-hong,TIAN Bao-dan.Realization on the Computer Algebra about Enumeration Formulas for the Number of Isomorphism Classes of Finite Groups[J].Journal of Sichuan University of Science & Engineering:Natural Science Editton,2008,21(4). |
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| Authors: | QIU Yan-hong TIAN Bao-dan |
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| Abstract: | It has been discussed in the Reference1] that if 1≤k≤1000,algorithm of Balass'enumeration formulas for the number of isomorphism classes of groups is obtained in the paper,and is realized by Matlab program.There are infinitely many solutions for f(n)=k.Also k is extended,that is if,there are infinitely many solutions for f(n)=k. |
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| Keywords: | finite group number of isomorphism classes of groups Balass' formula |
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