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MAT8023 群论及其应用 Group Theory and its Applications
课程学分/学时
Course Credit/Hours
是否面向本科生开放
Open to undergraduates
or not
( 如 面 向 本 科 生 开 放 , 请 注 明 区 分 内 容 。 If the course is open to
undergraduates, please indicate the difference.)
Abstract Algebra II, Permutation groups
MAT8020 抽象代数 II, MAT7078 置换群
(如 面 向 本 科 生开 放 , 请 注 明 区 分 内容 。 If the course is open to undergraduates, please indicate the
difference.)
让学生熟练掌握群论及对称图论的基本知识、方法,及其主流问题和重要问题;通过学习有限单
群分类定理,了解该领域的发展趋势。学生学习内容包括有限群的结构及群作用、有限域上的群表示
论、有限典型群的子群、群在图上的作用、图的对称性以及凯莱图的同构问题。
Students are supposed to understand basic knowledge and methods of group theory and symmetric graph
theory, as well as their mainstream and important problems. Students can also understand the development
tendency of group theory by learning the classification of finite simple groups. The main content includes
Structures and actions of finite groups,group representations over finite fields, subgroups of finite classical
groups, group actions on graphs and graph symmetries, and isomorphism problems for Cayley graphs.
(如面向本科生开放,请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.)
讲授, 讨论
教学内容
Course Contents
(如面向本科生开放,请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.)
有 限 群 的 结 构 和群作用 Structures and actions of finite groups (10 credit
hours)
群 在 有 限 域 上 的 表 示 Group representations over finite fields (10 credit
hours)
有限典型群的子群 Subgroups of finite classical groups (10 credit hours)
群 在 图 上 的 作 用 和 图 的 对 称 性 Group actions on graphs and graph
symmetries (10 credit hours)