| 内交换p群的中心扩张(Ⅳ) |
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| 引用本文： | 曲海鹏,郑丽峰.内交换p群的中心扩张(Ⅳ)[J].数学学报,2011(5). |
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| 作者姓名： | 曲海鹏 郑丽峰 |
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| 作者单位： | 山西师范大学数学与计算机科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(11071150); 山西省自然科学基金(2008012001); 山西省回国留学人员科研项目([2007]13-56) |
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| 摘 要： | 设N,H是任意的群.若存在群G,它具有正规子群≤Z(G),使得≌N且G/≌H,则称群G为N被H的中心扩张.本文完全分类了当N为p~3阶初等交换p群及H为内交换p群时,N被H的中心扩张得到的所有不同构的群.从而我们完全分类了初等交换p群被内交换p群的中心扩张得到的所有不同构的群.
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| 关 键 词： | 中心扩张 初等交换p群 内交换p群 |
The Central Extension of Inner Abelian p-Groups(Ⅳ) |
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| Hai Peng QU Li Feng ZHENG.The Central Extension of Inner Abelian p-Groups(Ⅳ)[J].Acta Mathematica Sinica,2011(5). |
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| Authors: | Hai Peng QU Li Feng ZHENG |
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| Institution: | Hai Peng QU Li Feng ZHENG Department of Mathematics of Shanxi Normal University,Linfen 041004,P.R.China |
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| Abstract: | Assume N and H are groups.If there is a group G which has a normal subgroup ≤Z(G) such that ≌N and G/≌H,then G is called a central extension of N by H.In this paper,we classified all groups which are central extensions of N by H,where N is an elementary abelian p-group of order p~3 and H is an inner abelian p-group.Thus all groups which are central extensions of an elementary abelian p-group by an inner abelian p-group are classified. |
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| Keywords: | central extension elementary abelian p-groups inner abelian p-groups |
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