| 关于72阶群的同构分类 |
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| 引用本文： | 陈松良,;蒋启燕,;莫贵圈,;崔忠伟.关于72阶群的同构分类[J].商丘师范学院学报,2014(9):4-9. |
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| 作者姓名： | 陈松良 ;蒋启燕 ;莫贵圈 ;崔忠伟 |
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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项目（黔科合J字[-2013]2234号）,贵州师范大学教学改革课题 |
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| 摘 要： | 设G是72(即23·32)阶群,采用新的方法对群G进行了完全分类,证明了G共有50种不同构的类型:若Sylow子群都正规,则G有10种;若Sylow 2-子群正规而Sylow 3-子群不正规,则G有4种;若Sylow 3-子群正规而Sylow 2-子群不正规,则G有32种;若Sylow子群都不正规,则G有4种.
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| 关 键 词： | 有限群 同构分类 群的构造 |
On the structures of groups of order 72 |
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| Institution: | CHEN Songliang, JIANG Qiyan, MO Guiquan, CUI Zhongwei ( 1. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China; 2. School of Mathematics and Computer Science, Guizhou Normal College, Guiyang 550018,China) |
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| Abstract: | Let G be finite groups of order 72 （ i.e.23 · 32 ）.In this paper, we have showed that G has 50 nonisomorphic types,i.e.1）If every Sylow subgroup is normal , G has 10 nonisomorphic types;2） If every Sylow 2-subgroup is normal and every Sylow 3-subgroup is non -normal, G has 4 nonisomorphic types;3 ） If every Sylow 3-subgroup is normal and every Sylow 2-subgroup is non -normal, G has 32 nonisomorphic types;4） If every Sylow subgroup is non -normal , G has 4 nonisomorphic types . |
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| Keywords: | finite group isomorphic classification structure of group |
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