关于半直积的同构

关于半直积的同构 On the Isomorphism of the Semidirect Product 刘修生 LIU Xiu-sheng 1 1 2 3 first-author 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 School of Mathematics and Statistics, Wuhan University School of Mathematics and Statistics, Wuhan University 黄石高等专科学校公共课部 黄石高等专科学校公共课部 Department of Basic Courses, Huangshi Polytechnic College Department of Basic Courses, Huangshi Polytechnic College ,湖北,黄石,435003 ,湖北,黄石,435003 设N ,H是两个群 ,φ ,ψ分别是从群H到N的自同构群Aut（N）的两个自同态 ,本文证明了当群H及同态映射 φ ,ψ满足一定条件下半直积NφH与半直积NψH同构的三个定理 ,而其中两个定理包括了已知的两个结果 . Let N,H be two groups, and φ,ψ be two homomorphism from H to Aut（N） of the automorphism group of N. In this paper, we give some condition under which we prove three theorems about the isomorphism between the semidirect product of N by H corresponding to φ and that of N by H corresponding to ψ.Two of the theorems extend two well-known results, respectively. 同构 半直积 循环群 克莱茵四元群 isomorphism semidirect product cyclic group Klein group of the four elements O152.1 国家基础科学发展计划 （ 973计划 ）基金资助项目 2003-03-01 2021-04-01 3