内交换p-群的中心扩张(I)

李立莉, 曲海鹏, 陈贵云

数学学报 ›› 2010, Vol. 53 ›› Issue (4) : 675-684.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2010, Vol. 53 ›› Issue (4) : 675-684. DOI: 10.12386/A2010sxxb0075
论文

内交换p-群的中心扩张(I)

    李立莉1, 曲海鹏2, 陈贵云1
作者信息 +

Central Extension of Inner Abelian p-Groups (I)

    Li Li LI1, Hai Peng QU2, Gui Yun CHEN1
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文章历史 +

摘要

设N,H为群. H被N的中心扩张是关于群的短正合序列:满足N≤Z(G).本文完全分类了当|N|=p,H为内交换p-群时, H被N的中心扩张所得的群.  

Abstract

Let H,N be finite groups. An central extension of H by N is that a short exact sequence of groups： satisfys N≤Z(G). In this article, we classify completely the groups central extention of H by N gets, when |N|=p and H is an inner abelian p-group.  

关键词

内交换p-群 / 中心扩张 / 亚交换群

Key words

inner abelian p-group / central extension / metabelian group

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李立莉, 曲海鹏, 陈贵云. 内交换p-群的中心扩张(I). 数学学报, 2010, 53(4): 675-684 https://doi.org/10.12386/A2010sxxb0075
Li Li LI, Hai Peng QU, Gui Yun CHEN. Central Extension of Inner Abelian p-Groups (I). Acta Mathematica Sinica, Chinese Series, 2010, 53(4): 675-684 https://doi.org/10.12386/A2010sxxb0075

参考文献



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[4] Rédei L., Das schiefe Product in der Gruppentheorie, Comment. Math. Helvet., 1947, 20: 225--267.



[5] An L. J., Finite p-Groups All of Whose Non-abelian Proper Subgroups are Generated by Two Elements, Xi'an: Master Thesis, Shanxi Normal University, 2006.



[6] Hölder O., Die Gruppen der Ordnungen p3, pq2, pqr, p4, Math. Ann., 1893, 43: 301--412.



[7] James R., The groups of order p6, (p≥3), Mathematics of Computation, 1980, 34: 613--637.



[8] Xu M. Y., A theorem about p-groups and some consequences, Chin. Ann. Math., 1984, 5B: 1--6.

基金

国家自然科学基金(10771172);数学天元基金(10926030);西南大学研究生科技创新基金(10414020711604)

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