内交换p群的中心扩张(Ⅳ)  

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

作　　者：曲海鹏[1] 郑丽峰[1] 

机构地区：[1]山西师范大学数学与计算机科学学院,临汾041004

出　　处：《数学学报（中文版）》2011年第5期739-752,共14页Acta Mathematica Sinica：Chinese Series

基　　金：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)

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.Assume N and H are groups. If there is a group G which has a normal subgroup N 〈 Z（G） such that N ≈ N and GIN ≈ 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 p3 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.

关 键 词：中心扩张 初等交换p群 内交换p群 

分 类 号：O152[理学—数学]