| pq~3阶群的完全分类 |
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| 引用本文： | 陈松良,欧阳建新,李惊雷.pq~3阶群的完全分类[J].海南师院学报,2010(3):253-255,263. |
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| 作者姓名： | 陈松良 欧阳建新 李惊雷 |
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| 作者单位： | 贵州师范学院数学与计算机科学学院,贵州贵阳550018 |
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| 基金项目： | 贵州省科技厅自然科学基金资助项目（2010GZ77391）; 贵州师范学院自然科学基金项目（200901006） |
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| 摘 要： | 设p,q均为素数,且p〉q,对pq3阶群进行了完全分类并获得了其全部构造：1）当q不整除p-1且p不整除（q2＋q＋1）时,G恰有5个彼此不同构的类型;2）当q不整除p-1但p整除（q2＋q＋1）时,G恰有6个彼此不同构的类型;3）当q整除p-1但q2不整除p-1且p不整除（q2＋q＋1）时,G恰有12个彼此不同构的类型;4）当q整除p-1且p整除（q2＋q＋1）但q2不整除p-1时,G恰有13个彼此不同构的类型;5）当q2整除p-1但q3不整除p-1时,G恰有14个彼此不同构的类型;6）当q3整除p-1时,G恰有15个彼此不同构的类型.
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| 关 键 词： | 有限群 同构分类 群的表写 |
Classification of Finite Groups of Order pq~3 |
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| CHEN Songliang,OUYANG Jianxin,LI Jinglei.Classification of Finite Groups of Order pq~3[J].Journal of Hainan Normal University(Humanities and Social Sciences),2010(3):253-255,263. |
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| Authors: | CHEN Songliang OUYANG Jianxin LI Jinglei |
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| Institution: | (School of Mathematics and Computer Science, Guizhou Normal College,Guiyang 550018,China) |
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| Abstract: | Letting p,q be odd primes such that pq, letting G be a finite group of order pq3, the isomorphic classification of G were discussed, and their presentations are completely described.We have showed that：1） If q doesn＇t divide （p-1） and p doesn＇t divide （q2＋q＋1）, G has 5 nonisomorphic presentations; 2） If q doesn＇t divide （p-1） and p divides （q2＋q＋1）, G has 6 nonisomorphic presentations; 3） If q divides （p-1） and q2 doesn＇t divide （p-1） and p doesn＇t divide （q2＋q＋1）, G has 12 nonisomorphic presentations; 4） If q divides （p-1）） and q2 doesn＇t divide （p-1） and p divides （q2＋q＋1）, G has 13 nonisomorphic presentations; 5） If q2 divides （p-1） and q3 doesn＇t divide （p-1）, G has 14 nonisomorphic presentations; 6） If q3 divides（p-1）, G has 15 nonisomorphic presentations. |
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| Keywords: | finite group isomorphic classification presentation of group |
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