| 模n整数U-群的性质 |
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| 引用本文： | 杨志强,任北上. 模n整数U-群的性质[J]. 广西师范学院学报(自然科学版), 2005, 22(1): 113-116,120 |
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| 作者姓名： | 杨志强 任北上 |
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| 作者单位： | 广西师范学院,数学与计算机科学系,广西,南宁,530001;广西师范学院,数学与计算机科学系,广西,南宁,530001 |
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| 基金项目： | TheprojectwassupportedbytheNaturalScienceFoundationofGuangxi(0 4 4 70 38) |
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| 摘 要： | 模n整数U-群是一类重要的交换乘群,它为我们更好地表述群的类似外直积与内直积相互关系的一些代数特征提供了极其简便的方法.该文讨论了模n整数U-群的基本性质并推出论证了群论中的重要等式U(st)=Us(st)×Ut(st)≌U(t)(+)U(s).
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| 关 键 词： | 模n整数U-群 外直积 内直积 互素 |
The Properties of U-group of Integers Modulo n |
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| YANG Zhi-qiang,REN Bei-shang. The Properties of U-group of Integers Modulo n[J]. Journal of Guangxi Teachers Education University:Natural Science Edition, 2005, 22(1): 113-116,120 |
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| Authors: | YANG Zhi-qiang REN Bei-shang |
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| Abstract: | U-group, the group of units modulo n is a commutative multiplication group, it provides a convenient way to illustrate the algebraic ideas of groups and to clarify the distinction between internal and external direct products. The important equality U(st)=Us(st)×Ut(st)≌U(t)(+)U(s) which joins external direct products and internal direct products is proved. In this paper, the properties and deepen use of U-group is introduced, we prove a rather perfect result. |
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| Keywords: | U-group of integers modulo n external direct product internal direct product relatively prime |
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