| 用子群个数刻画有限群 |
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| 引用本文： | 陈云坤.用子群个数刻画有限群[J].贵州大学学报(自然科学版),2011,28(3):1-3,10. |
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| 作者姓名： | 陈云坤 |
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| 作者单位： | 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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| 摘 要： | 子群的个数对有限群有很大的影响,不少群论工作者对此也有很多的研究,本文利用子群的个数给出几类有限群的新刻画,当|G| =2p；22p(p＞3,P为奇素数),3p2 (p＞3,p为奇素数且3不整除p-1)时,G可由子群的个数唯一确定.
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| 关 键 词： | 子群的个数 正规子群 同构 可解群 |
Characterization of a Number of Subgroups of Finite Groups |
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| CHEN Yun-kun.Characterization of a Number of Subgroups of Finite Groups[J].Journal of Guizhou University(Natural Science),2011,28(3):1-3,10. |
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| Authors: | CHEN Yun-kun |
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| Institution: | CHEN Yun-kun1,2(1.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China;2.School of Mathematics Suzhou University,Suzhou 215006,China) |
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| Abstract: | The number of subgroups has much influence of the structures of finite groups.Many researchers of the group theory have studied a lot.a new characterization of some finite groups was studied by the number of their subgroups,that is when |G|=2p,p is odd prime;22 p,p is a odd prime;3 p2(p>3,p is a prime,3 doesn’t divide p-1),then G is only determined by m. |
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| Keywords: | the number of subgroups normal subgroup isomorphic solvable groups |
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