UC知道英语手动翻译高手进---十万个感谢
来源：百度知道 编辑：UC知道 时间：2024/06/27 04:37:50
摘 要
对称群的子群以及子群的结构的研究是群论中非常重要的课题, 长期以来, 对称群的理论研究已经取得了很大的成果, 由于科学技术的不断进步, 特别是计算机的发展与推广, 对称群的理论与方法的应用日臻广泛, 不仅在数学的各个分支上有应用, 而且在计算机科学, 系统工程, 现代物理, 化学, 通信科学上都有应用, 因此, 对称群有很大的实际应用价值.
本文主要研究低阶对称群的子群和低阶对称群的不变子群, 对于低阶对称群的子群的研究, 主要研究了和的子群的个数以及子群的构造, 通过Lagrange定理, 按照子群的阶的秩序给出了的全部30个字群, 构造性地给出了的一些子群. 对于低阶对称群的不变子群, 主要研究了对称群的换位子群和的单性以及的阶子群, 通过对这些内容的研究, 对低阶对称群的子群和不变子群有了更深刻的认识.
关键词： 对称群; 子群; 不变子群; 单性
substract:
The study of symmetry group's subgroup and the structure of subgroup is a very important subject in Group theory . For a long time , the theory study on symmetry group has got great achievements . As for the instant progress of science and technology , especially the development and popularization of computer , the application of theory and method of symmetry group is gradually widespreaded : not only be applied in branches of mathematics , but also be applied in computer science , systems engineering , modern physics , chemistry and communication science . Therefore , symmetry group has great value in practical application .
This paper mainly studies the low-symmetry group and the unchanged subgroup of it . For the study of subgroup of low-symmetry group , it mainly studies the quantity and the structure of these subgroups . Through Lagrange Theorem , totally 30 subgroups were given according to the order of the subgroups' rank , and some subgroups wer