| 有限p-群可交换的若干条件 |
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| 引用本文： | 何美,刘小川.有限p-群可交换的若干条件[J].山西大同大学学报（自然科学版）,2012,28(1):9-10,51. |
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| 作者姓名： | 何美 刘小川 |
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| 作者单位： | 山西大同大学数学与计算机科学学院,山西大同,037009 |
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| 摘 要： | 有限交换群可以分解成若干有限p-群的直积,有限p-群的交换性在研究有限群中起到重要作用。通过对有限p-群子群的分析,得到若干有限p-群可交换的条件,特别地得到,有限p-群是循环群的一个定理:|G|=pn,N是G的唯一p阶子群,G/N是交换群,p>2,则G是循环群。
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| 关 键 词： | 有限p-群 交换群 循环群 |
Several Sufficient Conditions of a Finite p-group be an Abelian Group |
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| HE mei
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LIU Xiao-chuan.Several Sufficient Conditions of a Finite p-group be an Abelian Group[J].Journal of Shanxi Datong University(Natural Science Edition),2012,28(1):9-10,51. |
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| Authors: | HE mei LIU Xiao-chuan |
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| Institution: | (School of Mathematic and Computer Science,Shanxi Datong University,Datong Shanxi,037009) |
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| Abstract: | An abelian Group is a direct product of several limited p-group.The abelian property of finite p-group plays an important role in studying finite group.According to analyzing subgroup of finite p-group,several conditions of abelian finite p-group have been gotten,especially,a theorem that a finite p-group is a cyclic group is gotten: |G|=pn,N is the unique p-order subgroup of G,G / N is an abelian group,if p > 2,G is a cyclic group. |
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| Keywords: | finite p-group abelian group cyclic group |
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