置换群的符号表示:Stick符号  

The symbolic representation of permutation groups:Stick notation

作　　者：沈尧[1] 周池春 陈玉柱 SHEN Yao;ZHOU Chi-chun;CHEN Yu-zhu(School of Criminal Investigation,People’s Public Security University of China,Beijing 100038,China;School of Engineering,Dali University,Dali,Yunnan 871003,China;School of Physical Science and Technology,Tiangong University,Tianjin 300387,China)

机构地区：[1]中国人民公安大学侦查学院,北京100038 [2]大理大学工程学院,云南大理871003 [3]天津工业大学,物理科学与技术学院,天津300387

出　　处：《大学物理》2025年第2期20-23,共4页College Physics

基　　金：中央高校基本科研业务费专项资金(2022JKF02024)资助;国家自然科学基金(62106033)资助。

摘　　要：群论教学是物理教学的重要组成部分,置换群则是离散群教学的最核心内容.群的概念深刻且复杂,传统教学中的符号表示和基于矩阵的群表示不够直观,这些都使初学者难以掌握群论的核心概念.群论教学中需要一种更直观、更有启发性的新方法,帮助初学者更容易领会与群有关的基本概念.在本文中,我们引入一种不同的符号表示,称之为Stick符号表示,并且重点以3阶置换群为例进行介绍.这些符号能够直观展示群元作用、共轭、对易、子群和不变子群等基本概念,是一个有趣的新工具,能够有效提升群论教学效率.Group theory is a crucial component of physics teaching,with permutation groups being central to discrete group instruction.The concept of groups is profound and complex,and traditional symbolic and matrix-based representations used in teaching are often not intuitive.This makes it difficult for beginners to grasp the core concepts of group theory.Therefore,there is a necessary for a more intuitive and enlightening method in group theory education to help beginners more easily understand fundamental group-related concepts.In this paper,we introduce an alternative symbolic representation called Stick notation,focusing on the example of the 3-order permutation group.These symbols can intuitively demonstrate essential concepts such as group action,conjugation,commutativity,subgroups,and invariant subgroups.This new and engaging tool has the potential to significantly enhance the effectiveness of group theory education.

关 键 词：群论 群表示 置换群 符号表示 

分 类 号：O414-21[理学—理论物理]