| 关于Sylow p-子群循环的12p~n阶群的构造 |
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| 引用本文： | 陈松良,蒋启燕. 关于Sylow p-子群循环的12p~n阶群的构造[J]. 烟台大学学报(自然科学与工程版), 2013, 0(3): 157-159 |
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| 作者姓名： | 陈松良 蒋启燕 |
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| 作者单位： | [1]贵州师范学院数学与计算机科学学院,贵州贵阳550018 [2]贵州师范大学数学与计算机科学学院,贵州贵阳550001 |
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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）. |
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| 摘 要： | 设p为奇素数,且p5,对Sylow p-子群循环的12pn阶群进行了完全分类并获得了其全部构造:1)当p≡1(mod 12)时,G恰有16个彼此不同构的类型;2)当p≡5(mod12)时,G恰有10个彼此不同构的类型;3)当p≡7(mod 12)时,G恰有14个彼此不同构的类型;4)当p≡11(mod 12)时,G恰有9个彼此不同构的类型.
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| 关 键 词： | 有限群 同构分类 群的构造 |
On the Structure of Finite Groups of Order 12p^n Whose Sylow Subgroups are Cyclic |
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| CHEN Song-liang,JIANG Qi-yan. On the Structure of Finite Groups of Order 12p^n Whose Sylow Subgroups are Cyclic[J]. Journal of Yantai University(Natural Science and Engineering edirion), 2013, 0(3): 157-159 |
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| Authors: | CHEN Song-liang JIANG Qi-yan |
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| Affiliation: | 1. School of Mathematics and Computer Science, Guizhou Normal College, Guiyang 550018, China;2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China) |
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| Abstract: | Let p be an odd prime and G be finite groups of order 12p^n such that p 〉 5. In this paper, we classify and determine the structure of G, i. e. , we show that： If 12 divides （p - 1 ） , then there are 16 nonisomorphic classes; if 12 divides （p -5 ） , then 10 nonisomorphic classes ,if 12 divides （p-7） ,then 14 monisomorphie classes and if 12 divides （p-11 ） then 9 nonisomorphic classes. |
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| Keywords: | finite group isomorphic classification structure of group |
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