群论导论第4版

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作　者：	（美）罗曼著
出版社：	世界图书出版公司
丛编项：
标　签：	组合理论

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ISBN：	9787510004988	出版时间：	2009-08-01	包装：	平装
开本：	24开	页数：	513	字数：

内容简介

　　《群论导论（第4版）（英文版）》介绍了：Group Theory is a vast subject and， in this Introduction （as well as in theearlier editions）， I have tried to select important and representative theoremsand to organize them in a coherent way. Proofs must be clear， and examplesshould illustrate theorems and also explain the presence of restrictive hypo-theses. ！ also believe that some history should be given so that one canunderstand the origin of problems and the context in which the subjectdeveloped.Just as each of the earlier editions differs from the previous one in a signifi-cant way， the present （fourth） edition is genuinely different from the third.Indeed， this is already apparent in the Table of Contents. The book nowbegins with the unique factorization of permutations into disjoint cycles andthe parity of permutations; only then is the idea of group introduced. This isconsistent with the history of Group Theory， for these first results on permu-tations can be found in an 1815 paper by Cauchy， whereas groups of permu-tations were not introduced until 1831 （by Galois）But even if history

作者简介

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图书目录

Preface to the Fourth Edition
From Preface to the Third Edition
To the Reader
CHAPTER 1　Groups and Homomorphisms
　Permutations
　Cycles
　Factorization into Disjoint Cycles
　Even and Odd Permutations
　Semigroups
　Groups
　Homomorphisms
CHAPTER 2　The Isomorphism Theorems
　Subgroups
　Lagrange's Theorem
　Cyclic Groups
　Normal Subgroups
　Quotient Groups
　The Isomorphism Theorems
　Correspondence Theorem
　Direct Products
CHAPTER 3　Symmetric Groups and G-Sets
　Conjugates
　Symmetric Groups
　The Simplicity of A.
　Some Representation Theorems
　G-Sets
　Counting Orbits
　Some Geometry
CHAPTER 4　The Sylow Theorems
　p-Groups
　The Sylow Theorems
　 Groups of Small Order
CHAPTER 5　Normal Series
　 Some Galois Theory
　 The Jordan-Ho1der Theorem
　 Solvable Groups
　 Two Theorems of P. Hall
　 Central Series and Nilpotent Groups
　 p-Groups
CHAPTER 6　Finite Direct Products
　 The Basis Theorem
　 The Fundamental Theorem of Finite Abelian Groups
　 Canonical Forms; Existence
　 Canonical Forms; Uniqueness
　 The KrulI-Schmidt Theorem
　 Operator Groups
CHAPTER 7　Extensions and Cohomology
　 The Extension Problem
　 Automorphism Groups
　 Semidirect Products
　 Wreath Products
　 Factor Sets
　 Theorems of Schur-Zassenhaus and GaschiJtz
　 Transfer and Burnside's Theorem
　 Projective Representations and the Schur Multiplier
　 Derivations
CHAPTER 8　Some Simple Linear Groups
……
CHAPTER 9　Permutations and the Mathieu Groups
CHAPTER 10　Abelian Groups
CHAPTER 11　Free Groups and Free Products
CHAPTER 12　The Word Problem
Epilogue
Bibliography
Notation
Index