有限群直积的自同构群  

Automorphism Group of Direct Product of Finite Groups

作　　者：秦鑫[1] 雒晓良[1] 

机构地区：[1]吕梁学院数学系,山西离石033000

出　　处：《山西大同大学学报（自然科学版）》2011年第4期13-16,共4页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：国家自然科学基金资助项目[10771132]

摘　　要：设G=H×K为有限群H和K的直积,由Bidwell等定义了AutG的四个特殊子群A,B,C,D满足A≌AutH,B≌Hom(H,Z(K)),C≌Hom(K,Z(H)),D≌AutK并且证明了一个重要结果:如果H和K没有同构的直因子,则AutG=ABCD。在此基础上进一步研究得到了AutG=ABCD的一个简明的充要条件。Let G=HxK be the direct product of finite groups H and K. In the paper published by Bidwell, Curran and McCaugh- an in 2006, four special subgroups A, B, C, D of AutG were defined firstly, which satisfy and then an important result that AutG=ABCD if H and K have no common direct factor was proven. In this paper a necessary and sufficient condition is given for AutG=ABCD.

关 键 词：群的直积 自同构 自同态 矩阵表示 

分 类 号：O152.1[理学—数学]