极大类2群的2次中心扩张  

The Central Extension of Degree 2 By A 2-Group of Maximal Class

作　　者：王亮亮[1] 李有连[2] 

机构地区：[1]吕梁学院数学系,山西离石033000 [2]吕梁学院离石师范分校数学系,山西离石033000

出　　处：《数学的实践与认识》2013年第23期231-236,共6页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(2012011001-3);山西省回国留学人员科研项目([2011]8-59)

摘　　要：设N,H是任意的群.若存在群G,它有正规子群N≤Z(G),使得N≌N且G/N√≌H,则称群G为N被H的中心扩张.完全分类了当N为2阶循环群及H为极大类2群时,N被H的中心扩张得到的所有互不同构的群.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 G｜N=H, 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 group of order p and H is a maximal class 2-groups.

关 键 词：极大类2群 二面体群 广义四元数群 半二面体群 

分 类 号：O152.1[理学—数学]