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简介
有限群理论以在论述上简明、但在论证上简单而引人注目，并且以基础的方式应用于数学的多个分支，例如数论。《有限群导引》（英文版）给出了有限群简明、基础的介绍，以最大限度地服务初学者和数学家。本书共10章，每章都配备了一系列的练习。
目录
Preface
Conventions and Notation
1 Preliminaries
1.1 Group actions
1.2 Normal subgroups, automorphisms, characteristic subgroups, simple groups
1.3 Filtrations and Jordan-H？lder theorem
1.4 Subgroups of products: Goursat’s lemma and Ribet’s lemma
1.5 Exercises
2 Sylow theorems
2.1 Definitions
2.2 Existence of p-Sylow subgroups
2.3 Properties of the p-Sylow subgroups
2.4 Fusion in the normalizer of a p-Sylow subgroup
2.5 Local conjugation and Alperin’s theorem
2.6 Other Sylow-like theories
2.7 Exercises
3 Solvable groups and nilpotent groups
3.1 Commutators and abelianization
3.2 Solvable groups
3.3 Descending central series and nilpotent groups
3.4 Nilpotent groups and Lie algebras
3.5 Kolchin’s theorem
3.6 Finite nilpotent groups
3.7 Applications of 2-groups to field theory
3.8 Abelian groups
3.9 The Frattini subgroup
3.10 Characterizations using subgroups generated by two elements
3.11 Exercises
4 Group extensions
4.1 Cohomology groups
4.2 A vanishing criterion for the cohomology of finite groups
4.3 Extensions, sections and semidirect products
4.4 Extensions with abelian kernel
4.5 Extensions with arbitrary kernel
4.6 Extensions of groups of relatively prime orders
4.7 Liftings of homomorphisms
4.8 Application to p-adic liftings
4.9 Exercises
5 Hall subgroups
5.1 π-subgroups
5.2 Preliminaries: permutable subgroups
5.3 Permutable families of Sylow subgroups
5.4 Proof of theorem 5.1
5.5 Sylow-like properties of the π-subgroups
5.6
...... 全部内容请购买实物书籍
Conventions and Notation
1 Preliminaries
1.1 Group actions
1.2 Normal subgroups, automorphisms, characteristic subgroups, simple groups
1.3 Filtrations and Jordan-H？lder theorem
1.4 Subgroups of products: Goursat’s lemma and Ribet’s lemma
1.5 Exercises
2 Sylow theorems
2.1 Definitions
2.2 Existence of p-Sylow subgroups
2.3 Properties of the p-Sylow subgroups
2.4 Fusion in the normalizer of a p-Sylow subgroup
2.5 Local conjugation and Alperin’s theorem
2.6 Other Sylow-like theories
2.7 Exercises
3 Solvable groups and nilpotent groups
3.1 Commutators and abelianization
3.2 Solvable groups
3.3 Descending central series and nilpotent groups
3.4 Nilpotent groups and Lie algebras
3.5 Kolchin’s theorem
3.6 Finite nilpotent groups
3.7 Applications of 2-groups to field theory
3.8 Abelian groups
3.9 The Frattini subgroup
3.10 Characterizations using subgroups generated by two elements
3.11 Exercises
4 Group extensions
4.1 Cohomology groups
4.2 A vanishing criterion for the cohomology of finite groups
4.3 Extensions, sections and semidirect products
4.4 Extensions with abelian kernel
4.5 Extensions with arbitrary kernel
4.6 Extensions of groups of relatively prime orders
4.7 Liftings of homomorphisms
4.8 Application to p-adic liftings
4.9 Exercises
5 Hall subgroups
5.1 π-subgroups
5.2 Preliminaries: permutable subgroups
5.3 Permutable families of Sylow subgroups
5.4 Proof of theorem 5.1
5.5 Sylow-like properties of the π-subgroups
5.6
...... 全部内容请购买实物书籍
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