子群的陪集与群的同构定理的几何解释  

Geometric Interpretation of Coset of Subgroups and Isomorphism Theorem of Groups

作　　者：高印芝[1,2] 袁兰党 GAO Yinzhi;YUAN Landang(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Hebei International Joint Research Center for Mathematics and Interdisciplinary Science,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024 [2]河北省数学与交叉科学国际联合中心,石家庄050024

出　　处：《大学数学》2022年第3期97-100,共4页College Mathematics

基　　金：河北师范大学教学改革项目(2019XJJG048)。

摘　　要：通过二维空间、三维空间、平面和直线等特殊的群,对子群的陪集、群的3个同构定理给予了几何解释,目的是对抽象的同构定理有更直观的认识.Through special groups,namely,three dimensional space,two dimensional space,planes and lines,geometric interpretation are given for the coset of subgroups and three isomorphism theorems of groups.The aim is to have a more intuitive understanding of the abstract isomorphism theorem.

关 键 词：群 子群 不变子群 商群 同构映射 

分 类 号：O151[理学—数学]