| 子群的指数集对有限群的影响 |
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| 引用本文： | 陈云坤.子群的指数集对有限群的影响[J].贵州师范大学学报(自然科学版),2011,29(1):45-47. |
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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;苏州大学数学科学学院,江苏苏州,215006 |
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| 摘 要： | 子群的指数是群的一个重要数量性质,主要研究子群的指数集合对有限群的影响,得出了如果两个群的子群的指数集合相等,若其中一个可解,则另一个也可解,且两个群的阶也相等,并对指数集合中的数字的连续性也进行了一定的研究.
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| 关 键 词： | 子群的阶 子群的指数 可解群 |
Effect of index sets of subgroups on finite groups |
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| CHEN Yun-kun.Effect of index sets of subgroups on finite groups[J].Journal of Guizhou Normal University(Natural Sciences),2011,29(1):45-47. |
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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,Guizhou 550001,China,2.School of Mathematics,Suzhou University,Suzhou,Jiangsu 215006,China) |
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| Abstract: | The order of finite group is an important quantity property.This paper mainly discusses the influence of index set of subgroups on finite groups,and gets that if index sets of subgroups of two groups are equal,where one group is solvable,then the other is also solvable,and their orders are equal.Moreover,this thesis studies the continuity of numbers in index set of subgroups of finite groups. |
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| Keywords: | orders of subgroups indexes of subgroups solvable groups |
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