The Central Extension of an Elementary Abelian p-Group by a Miniaml Non-Abelian p-Group  

作　　者：Lijian AN Le YANG 

机构地区：[1]Department of Mathematics, Shanxi Normal University

出　　处：《Journal of Mathematical Research with Applications》2016年第4期457-466,共10页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11371232;11471198)

摘　　要：Assume that N, F and G are groups. If there exsits N, a normal subgroup of G such that N ≌ G and GIN ≌ F, then G is called a central extension of N by F. In this paper, the central extension of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group of order p3. Together with our previous work, all central extensions of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group.Assume that N, F and G are groups. If there exsits N, a normal subgroup of G such that N ≌ G and GIN ≌ F, then G is called a central extension of N by F. In this paper, the central extension of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group of order p3. Together with our previous work, all central extensions of N by a minimal non-abelian p-group is determined, where N is an elementary abelian p-group.

关 键 词：central extension minimal non-abelian p-groups CONGRUENT 

分 类 号：O152.1[理学—数学]