| 李型单群C_n(3)的谱刻画 |
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| 引用本文： | 何怀玉.李型单群C_n(3)的谱刻画[J].辽宁工程技术大学学报(自然科学版),2012,31(3):409-412. |
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| 作者姓名： | 何怀玉 |
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| 作者单位： | 上海政法学院经济管理系,上海,201701 |
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| 基金项目： | 国家自然科学基金资助项目(10871032);上海市优青基金资助项目(szf10016) |
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| 摘 要： | 为找到有限单群所特有的算术性质,根据素图的连通分支,结合素图的连接标准,利用元素阶的集合,刻画了素图非连通的李型单群Cn(3)(其中n≠2),结果表明:对有限群G,若G与Cn(3)的元素的阶的集合相同,则G与Cn(3)同构,从而也证实了Kondratiev的猜想对李型单群Cn(3)也是成立的.该成果对有限群的数量刻画具有一定的参考价值和指导意义.
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| 关 键 词： | 有限群 单群 李群 谱 谱刻画 素图 本原素因子 孤立点数 |
Recognition of simple groups C_n(3) of Lie type by their spectrum |
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| HE Huaiyu.Recognition of simple groups C_n(3) of Lie type by their spectrum[J].Journal of Liaoning Technical University (Natural Science Edition),2012,31(3):409-412. |
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| Authors: | HE Huaiyu |
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| Institution: | HE Huaiyu(Department of Economics and Management,Shanghai University of Political Science and Law, Shanghai 201701,China) |
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| Abstract: | In order to find the special arithmetic properties of finite simple groups,according to the connected component of prime graph and the adjacency criterion for prime graph,the simple groups Cn(3)(where n≠2) of Lie type with disconnected prime graph are recognized by their element orders.The study found that every finite group G with the same set of element orders as Cn(3) is isomorphic to Cn(3).Also,Kondratiev’s conjecture is true to simple groups Cn(3).The study has a reference value and some significance to the recognizability of finite groups. |
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| Keywords: | finite group simple group group of Lie type spectrum recognition by spectrum prime graph primitive prime divisor independence number |
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