实数集上的一个变换群的结构  

The Structure of a Transformation Group on the Set of Real Numbers

作　　者：何纪[1] 陈秋一 

机构地区：[1]常州信息职业技术学院,江苏常州213164 [2]常州铁道高等职业技术学校,江苏常州213011

出　　处：《常州信息职业技术学院学报》2006年第1期43-44,48,共3页Journal of Changzhou College of Information Technology

摘　　要：根据平面直线的关系,给出实数集R上的一类线形变换τ(a,b):x→ax+b,a≠0,该线形变换构成一个非交换群TR。通过分析这个非交换群TR,找到它的所有的Abel子群;同时发现非交换群TR是一个Abel子群和正规Abel子群的半直积;最后,给出TR的所有Abel子群的几何意义和矩阵表达。This article produces a kind of linear transformation τ（a,b）：x→ax＋b,a≠0 on the set R of real numbers according to the relations of the plane in straight line, These linear transformations constitute a non-comutative group TR. By analyzing the non-comutative group TR, we can get all its Abelian subgroup. At the same time we discover the non-comutative group TR, is a semi-product of an Abelian subgroup by an Abelian normal subgroup. Finally, we give the meanings of them in the geometry and the theory of matrix of all the Abelian subgroups of TR.

关 键 词：线形变换 变换群 交换子群 半直积 

分 类 号：O152.2[理学—数学]