| 最高阶元素个数为40的非可解群的分类 |
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| 引用本文： | 杜祥林,刘学飞,王绍恒. 最高阶元素个数为40的非可解群的分类[J]. 数学研究及应用, 2008, 28(3): 733-739. DOI: 10.3770/j.issn.1000-341X.2008.03.021 |
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| 作者姓名： | 杜祥林 刘学飞 王绍恒 |
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| 作者单位： | 庆三峡学院数学与计算机科学学院, 重庆 404000;庆三峡学院数学与计算机科学学院, 重庆 404000;庆三峡学院数学与计算机科学学院, 重庆 404000 |
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| 基金项目： | 三峡学院基金(No.2007-sxxyyb-01). |
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| 摘 要： | 设$varphi$为群${rm Aut}(N)$的同态,记$H_varphitimes N$为群$N$借助于群$H$的半直积.设$G$为有限不可解群,本文证明: 若$G$中最高阶元素个数为40, 则$G$同构于下列群之一:(1)~$Z_{4varphi}times A_5$,,${rm ker}varphi=Z_2$; (2)~$D_{8varphi}times A_5,,{rm ker}varphi=Z_2times Z_2$; (3)~$G/N=S_5$, $N=Z(G)=Z_2$; (4)~$G/N=S_5$, $N=Z_2times Z_2,,Ncap Z(G)=Z_2$.
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| 关 键 词： | 最高阶元素 非可解群 单截断. |
| 收稿时间： | 2006-06-07 |
| 修稿时间： | 2007-03-23 |
Classification about Non-Solvable Groups with Exactly 40 Maximal Order Elements |
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| DU Xiang Lin,LIU Xue Fei and WANG Shao Heng. Classification about Non-Solvable Groups with Exactly 40 Maximal Order Elements[J]. Journal of Mathematical Research with Applications, 2008, 28(3): 733-739. DOI: 10.3770/j.issn.1000-341X.2008.03.021 |
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| Authors: | DU Xiang Lin LIU Xue Fei WANG Shao Heng |
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| Affiliation: | School of Mathematics and Computer Science, Chongqing Three Gorges University, Chongqing 404000, China |
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| Abstract: | Let $varphi$ be a homomorphism from a group $H$ to a group ${rm Aut}(N)$. Denote by $H_{varphi}times N$ the semidirect product of $N$ by $H$ with homomorphism $varphi$. This paper proves that: Let $G$be a finite nonsolvable group. If $G$ has exactly 40 maximal order elements, then $G$ is isomorphic to one of the following groups: (1)~$Z_{4varphi}times A_5$,,${rm ker}varphi=Z_2$; (2)~$D_{8varphi}times A_5,,{rm ker}varphi=Z_2times Z_2$; (3)~$G/N=S_5$, $N=Z(G)=Z_2$; (4)~$G/N=S_5$, $N=Z_2times Z_2,,Ncap Z(G)=Z_2$. |
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| Keywords: | maximal order element non-solvable group simple section. |
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