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作者： Geoff Smith等著
出 版 社：
出版时间： 2000-6-1字数：版次： 1页数： 255印刷时间： 2000/06/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9781852332358包装： 平装内容简介
The theory of groups is simultaneously a branch of abstract algebra and the study of symmetry. Designed to support a reader engaged in a first serious group theory course, or a mathematically mature reader approaching the subject for the first time, this book reviews the essentials. It recaps the basic definitions and results, up to and including Lagrange's Theorem, and then continues to explore topics such as the isomorphism theorems and group actions. Later chapters include material on chain conditions and finiteness conditions, free groups and the theory of presentations. In addition, a novel chapter of "entertainments" takes the basic theory and plays with it to obtain an assortment of results that will show a little of what can be done with the theoretical machinery. Adopting the slightly irreverent tone of Geoff Smith's previous book, Introductory Mathematics: Algebra and Analysis, this book is a key reference that will both stimulate and entertain its readers.
目录
Preface
Contents
List of Figures
The Greek Alphabet
1. The Elements
1.1 Basic Results
1.2 Where Do Groups Come From?
1.3 Cosets
1.4 Subgroup Generation
1.5 Finite Generation
2. Structure
2.1 Conjugacy
2.2 Normal Subgroups
2.3 Factor Groups
2.4 Kernels and Images
2.5 Isomorphisms
2.6 Internal Direct Products
2.7 Finite Abelian Groups
2.8 Finitely Generated Abelian Groups ...
2.9 Semi-direct Products
2.10 Wreath Products
3. Action
3.1 Permutation Groups
3.2 Conjugacy in the Symmetric Group
3.3 Group Actions
3.4 Orbits Form Partitions
3.5 Conjugacy Revisited
3.6 Enumeration
3.7 Group Theoretic Consequences
3.8 Finite p-groups
3.9 Multiple Transitivity and Primitivity
4. Entertainments
4.1 The Finite Case
4.2 Infinite Groups
4.2.1 Infinite Simple Groups
4.2.2 An Infinite Alternating Group
4.2.3 The Transfer Map
4.3 The Derived Group
5. Law
5.1 The Commutator Calculus
5.2 The Derived Group Revisited
5.3 Nilpotent Groups
5.4 Varieties of Groups
5.5 Upper and Lower Central Series
5.6 Soluble Groups
6. Presentations
6.1 Informalities
6.2 The Rational Numbers
6.2.1 The Rationals Mark I
6.2.2 The Rationals Mark II
6.3 Tigers
6.3.1 Free Groups
6.4 Presentations and Free Groups
6.4.1 Standard Sloppy Notation
6.4.2 Commutator Subgroups
6.4.3 Tietze Transformations
6.5 Decideability Problems
6.6 The Knuth-Bendix Procedure
6.7 Church-Rosser and Confluence
6.8 Normal Forms
6.9 knuth-bendix for strings
7. Appendix A:Fields
8. Appendix B:Relations and orderings
Further Reading
Solutions
Index
