Dummit《Abstract Algebra Third Edition 》Ⅰ

基本公理与示例 1.1 基本公理与示例 1.1 基本公理与示例 1.1 基本公理与示例 1.1 基本公理与示例 1.1 基本公理与示例

1.2 DIHEDRAL GROUPS 1.2 二面体群 An important family of examples of groups is the class of groups whose

对称群 设 $\Omega$ 为任何非空集合，令 ${S}{\Omega }$ 为所有从 $\Omega$ 到其自身的双射（即 $\Omega$ 的所有排列）的集合。集合 ${S}{\Omega }$

1.4 MATRIX GROUPS 1.4 矩阵群 In this section we introduce the notion of matrix groups where the coeffic

1.6 HOMOMORPHISMS AND ISOMORPHISMS 1.6 同态与同构 In this section we make precise the notion of when two

1.7 GROUP ACTIONS 1.7 群作用 In this section we introduce the precise definition of a group acting on a

2.1 DEFINITION AND EXAMPLES 2.1 定义与示例 One basic method for unravelling the structure of any mathemat

2.2 CENTRALIZERS AND NORMALIZERS, STABILIZERS AND KERNELS 2.2 centralized 和 normalizers，stabilizers

2.3 CYCLIC GROUPS AND CYCLIC SUBGROUPS 2.3 循环群和循环子群 Let $G$ be any group and let $x$ be any element

2.4 SUBGROUPS GENERATED BY SUBSETS OF A GROUP 2.4 子群由群的子集生成 The method of forming cyclic subgroups o

2.5 THE LATTICE OF SUBGROUPS OF A GROUP 2.5 一个群的子群格 In this section we describe a graph associated w

3.1 DEFINITIONS AND EXAMPLES 3.1 定义与示例 In this chapter we introduce the notion of a quotient group o

3.2 MORE ON COSETS AND LAGRANGE'S THEOREM 3.2 关于陪集和拉格朗日定理的更多内容 In this section we continue the study

3.3 THE ISOMORPHISM THEOREMS 3.3 同构定理 In this section we derive some straightforward consequences of

3.4 COMPOSITION SERIES AND THE HÖLDER PROGRAM 3.4 组合列与 Hölter 计划 The remarks in the preceding sectio

3.5 TRANSPOSITIONS AND THE ALTERNATING GROUP 3.5 逆序和对换群 Transpositions and Generation of ${S}_{n}$ 逆

4.1 GROUP ACTIONS AND PERMUTATION REPRESENTATIONS 4.1 群作用与置换表示 In this section we give the basic the

4.2 GROUPS ACTING ON THEMSELVES BY LEFT MULTIPLICATION — CAYLEY’S THEOREM 4.2 通过左乘法自身作用 — 凯莱定理 In th

4.3 GROUPS ACTING ON THEMSELVES BY CONJUGATION —THE CLASS EQUATION 4.3 自共轭作用下的群自身作用——类方程 In this sec

4.4 AUTOMORPHISMS 4.4 自同构 Definition. Let $G$ be a group. An isomorphism from $G$ onto itself is cal