内交换p群的中心扩张 (II)

曲海鹏, 张小红

数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 933-944.

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数学学报 ›› 2010, Vol. 53 ›› Issue (5) : 933-944. DOI: 10.12386/A2010sxxb0104
论文

内交换p群的中心扩张 (II)

    曲海鹏, 张小红
作者信息 +

The Central Extension of Inner Abelian p-Groups (II)

    Hai Peng QU, Xiao Hong ZHANG
Author information +
文章历史 +

摘要

N, H是任意的群. 若存在群G, 它具有正规子群ÑZ(G),使得ÑNG/ÑH, 则称群GNH的中心扩张. 本文完全分类了当N为循环p群, H为内交换p群时, NH的中心扩张得到的所有不同构的群.

 

Abstract

Assume N and H are groups. If there is a group G which has a normal subgroup Ñ≤ Z(G) such that ÑN and G/ÑH, then G is called a central extension of N by H. In this paper, we classify all groups which are central extensions of N by H, where N is a cyclic p-group and H is an inner abelian p-group.

 

关键词

中心扩张 / 循环p / 内交换p

Key words

central extensions / cyclic p-groups / inner abelian p-groups

引用本文

导出引用
曲海鹏, 张小红. 内交换p群的中心扩张 (II). 数学学报, 2010, 53(5): 933-944 https://doi.org/10.12386/A2010sxxb0104
HaiPeng QU, Xiao Hong ZHANG. The Central Extension of Inner Abelian p-Groups (II). Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 933-944 https://doi.org/10.12386/A2010sxxb0104

参考文献


[1] Robinson D. J. S., A Course in the Theory of Groups, New York: Springer-Verlag, 1980.

[2] Suzuki M., Group Theory I., New York: Springer-Verlag, 1982.

[3] Xu M. Y., Qu H. P., Zhang Q. H., Finite p-groups all of whose subgroups of index p2 are metacyclic, to appear in Acta Math. Sci.

[4] Zhang Q. H., Guo X. Q., Qu H. P., Xu M. Y., Finite groups which have many normal subgroups, J. Korean Math. Soc., 2009, 46(6): 1165--1178.

[5] Zhang Q. H., Li L. L., Xu M. Y., Finite p-groups all of whose quotient groups are abelian or inner-abelian, to appear in Comm. Alg.

[6] Miller G. A., Moreno H. C., Non-abelian groups in which every subgroup is abelian, Trans. Amer. Math. Soc., 1903, 4: 398--404.

[7] Rédei L., Das schiefe product in der Gruppentheorie, Comm. Math. Helv., 1947, 20: 225--267.

[8] Berkovich Y., Janko Z., Groups of Prime Power Order, Volume 1, Berlin, New York: Walter de Gruyter, 2004.

[9] Li L. L., Qu H. P., Chen G. Y., The central extension of inner abelian p-groups (I), Acta Mathematica Sinica, Chinese Series, 2010, 53(4): 675--684.

[10] Xu M. Y., Introduction to Finite Groups (I, II), Beijing: Beijing Science Press, 1999.

[11] Chen C. G., Inner Σ-groups, Outer Σ-groups and Minimal Non-Σ-groups, Chongqing: Southwest China Normal University Press, 1988.

[12] Xu M. Y., Beijing Finite p-Groups, Beijing: Peking University Press, 2009.

[13] An L. J., Finite p-Groups all of Whose Non-Abelian Proper Subgroups are Generated by Two Elements, Xi'an: Shanxi Normal University Master's Degree Paper, 2006.

基金

国家自然科学基金资助项目(10671114);山西省自然科学基金(2008012001)和山西省回国留学人员科研项目([2007]13-56)资助

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