摘要
设N,H是任意的群.若存在群G,它具有正规子群N≤Z(G),使得N≌N且G/N≌H,则称群G为N被H的中心扩张.本文完全分类了当N为循环p群,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.
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 p-group and H is an inner abelian p-group.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2010年第5期933-944,共12页
Acta Mathematica Sinica:Chinese Series
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)
山西省回国留学人员科研项目([2007]13-56)资助
关键词
中心扩张
循环p群
内交换p群
central extensions
cyclic p-groups
inner abelian p-groups