| 4次对称群S_4的子群个数及其证明 |
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| 引用本文： | 孙自行,崔方达. 4次对称群S_4的子群个数及其证明[J]. 阜阳师范学院学报(自然科学版), 2005, 22(4): 13-16,28 |
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| 作者姓名： | 孙自行 崔方达 |
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| 作者单位： | 阜阳师范学院,数学系,安徽,阜阳,236041 |
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| 摘 要： | 使用Lagrange定理及n次对称群的基本概念证明了4次对称群存在且只存在30个子群,并给出了每个子 群．其中,除去两个平凡的子群,另有9个2阶循环群;4个3阶循环群;3个4阶循环群;4个Klein4元群;4个S3(在 同构意义之下);3个8阶子群以及1个12阶子群．
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| 关 键 词： | 4次对称群 子群 Lagrange定理 群的阶 元素的阶 循环置换 |
| 文章编号： | 1004-4329（2005）04-0013-05 |
| 收稿时间： | 2005-09-11 |
| 修稿时间： | 2005-09-11 |
Number of Subgroups of 4-Letters Symmetric Group S4 and Its Provement |
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| SUN Zi-xing,CUI Fang-da. Number of Subgroups of 4-Letters Symmetric Group S4 and Its Provement[J]. Journal of Fuyang Teachers College:Natural Science, 2005, 22(4): 13-16,28 |
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| Authors: | SUN Zi-xing CUI Fang-da |
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| Affiliation: | Math. Dept. of Fuyang Teachers College, Fuyang 236041 ,China |
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| Abstract: | Using Lagrange's theorem and the concept of n-letters symmetric group,we have Proved the only existence 30 certainly subgroups of the 4-letters symmetric group S4, getting rid of 2 normal subgroups, it has 9 2-order cyclic subgroups , 4 3-order cyclic subgroups,3 4-order cyclic subgroups, 4 Klein 4-elements groups 4 S4 (at the time of isomorphic meaning), 3 8-elements groups and 1 A4. |
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| Keywords: | 4-letters symmetric group subgroups Lagrange's theorem order of group order of element cycle permutation. |
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