| 最高阶元素个数为4p~2的有限群是可解群 |
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| 引用本文： | 晏燕雄.最高阶元素个数为4p~2的有限群是可解群[J].河南师范大学学报(自然科学版),2012,40(4):5-8. |
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| 作者姓名： | 晏燕雄 |
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| 作者单位： | 西南大学数学与统计学院,重庆400715;重庆第二师范学院数学与信息工程系,重庆400067 |
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| 基金项目： | 国家自然科学基金，重庆市科委自然科学基金，重庆市教委资助项目 |
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| 摘 要： | 研究了最高阶元素个数对有限群结构的影响.运用群阶的素因子,k阶循环子群共轭类的长,以及K3-单群和K4-单群的有关结论,证明了最高阶元素个数为|M(G)|=4p2的有限群G是可解群,其中p是素数.
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| 关 键 词： | 有限群 可解群 元素的阶 m-型 |
Finite Groups with |M(G)|=4p2 Elements of Maximal Order Are Solvable |
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| YAN Yan-xiong.Finite Groups with |M(G)|=4p2 Elements of Maximal Order Are Solvable[J].Journal of Henan Normal University(Natural Science),2012,40(4):5-8. |
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| Authors: | YAN Yan-xiong |
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| Institution: | YAN Yan-xiong1,2(1.School of Mathematics and Finance,Southwest China University,Chongqing 400715,China;2.Deparment of Mathematics and Information Engineering,Chongqing University of Education,Chongqing 400067,China) |
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| Abstract: | Affection on the structure of finite group as the number of maximal order elements is discussed.It is proved that such finite groups with 4p2 maximal order elements are solvable by making use of corresponding results on K3-simple groups and K4-simple groups,as well as the prime factor of the order of a finite group and the length of the conjugate class of cyclic subgroups with order k,where p is a prime |
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| Keywords: | finite groups solvable groups the order of elements m-type |
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