| 关于循环群的子群的探讨 |
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| 引用本文： | 牟金保,张旭波. 关于循环群的子群的探讨[J]. 东莞理工学院学报, 2010, 17(3): 20-23 |
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| 作者姓名： | 牟金保 张旭波 |
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| 作者单位： | 西北大学,数学系数学与科学史研究中心,西安,710127;西安理工大学,数学系,西安,710054 |
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| 基金项目： | 国家自然科学基金,陕西省教育厅科研资助项目 |
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| 摘 要： | 群是抽象代数最基础的一个概念,而循环群是群论中最简单、最特殊的群。循环群的学习对群、环、域的进一步研究有着重要的意义。着重讨论了循环群子群所具有的性质,及子群与子群间的内在联系,并归纳和推导出循环群的交与并的重要结论。
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| 关 键 词： | 循环群 阶 同构 |
The Discussion about the Subgroup of Cyclic Group |
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| MOU Jin-bao,ZHANG Xu-bo. The Discussion about the Subgroup of Cyclic Group[J]. Journal of Dongguan Institute of Technology, 2010, 17(3): 20-23 |
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| Authors: | MOU Jin-bao ZHANG Xu-bo |
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| Affiliation: | MOU Jin-bao~1 ZHANG Xu-bo~2 (1.Research Center for the History of Mathematics , Science,Northwest University,Xi'an 710127,China,2.Department of Mathematics,Xi'an University of Technology,Xi'an 710054,China) |
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| Abstract: | Group theory is the most basic theory in the Abstract Algebra,and cyclic group is the simplest,most specific group.The learning of cyclic groups has a great significance for further study of group,rings,fields.The article focused on the nature of the subgroups of the cyclic group,the intrinsic link between subgroups and subgroups,an important conclusions about intersection and union of cyclic group generalized and deduced. |
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| Keywords: | cyclic group the order isomorphic |
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