群论导论（第4版）（英文版） [An Introduction to the Theory of Groups] 下载 mobi epub pdf 电子书 2025

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《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

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
Lagranges Theorem
Cycic 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 Burnsides Theorem
Projective Representations and the Schur Multiplier
Derivations

CHAPTER 8
Some Simple Linear Groups
Finite Fields
The General Linear Group
PSL(2， K)
PSL(m， K)
Classical Groups

CHAPTER 9
Permutations and the Mathieu Groups
Multiple Transitivity
Primitive G-Sets
Simplicity Criteria
Atline Geometry
Projeetive Geometry
Sharply 3-Transitive Groups
Mathieu Groups
Steiner Systems

CHAPTER 10
Abelian Groups
Basics
Free Abelian Groups
Finitely Generated Abelian Groups
Divisible and Reduced Groups
Torsion Groups
Subgroups of
Character Groups

CHAPTER 11
Free Groups and Free Products
Generators and Relations
Semigroup Interlude
Coset Enumeration
Presentations and the Schur Multiplier
Fundamental Groups of Complexes
Tietzes Theorem
Covering Complexes
The Nielsen Schreier Theorem
Free Products
The Kurosh Theorem
The van Kampen Theorem
Amalgams
HNN Extensions

CHAPTER 12
The Word Problem
Introduction
Turing Machines
The Markov-Post Theorem
The Novikov-Boone-Britton Theorem： Sufficiency of Boones
Lemma
Cancellation Diagrams
The Novikov-Boone-Britton Theorem： Necessity of Boones
Lemma
The Higman Imbedding Theorem
Some Applications
Epilogue
APPENDIX I
Some Major Algebraic Systems
APPENDIX II
Equivalence Relations and Equivalence Classes
APPENDIX Ill
Functions
APPENDIX IV
Zorns Lemma
APPENDIX V
Countability
APPENDIX VI
Commutative Rings
Bibliography
Notation
Index

前言/序言

　　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 wereotherwise， I feel that it is usually good pedagogy to introduce a generalnotion only after becoming comfortable with an important special case. Ihave also added several new sections， and I have subtracted the chapter onHomologieal Algebra （although the section on Horn functors and charactergroups has been retained） and the section on Grothendieck groups.　The format of the book has been changed a bit： almost all exercises nowoccur at ends of sections， so as not to interrupt the exposition. There areseveral notational changes from earlier editions： I now write insteadof　to denote "H is a subgroup of G"; the dihedral group of order2n is now denoted by　instead of by ; the trivial group is denoted by ！instead of by {1}; in the discussion of simple linear groups， I now distinguishelementary traesvections from more general transvections;

群论导论（第4版）（英文版） [An Introduction to the Theory of Groups] 下载 mobi epub pdf txt 电子书 格式

评分☆☆☆☆☆

GTM系列的，这本群论书比较好读，作者写得很贴心。

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很好很酷啊

评分☆☆☆☆☆

GTM系列的，这本群论书比较好读，作者写得很贴心。

评分☆☆☆☆☆

我们可以把罗特曼的论证概括如下：个体数学家通过语言的媒介交流思想。作为讨论的结果，他们对数学概念的表达形式取得一致，而且这些表达形式在时间过程中可以发生变化。皮亚杰低估了数学家使用的语言，宁愿乞求·认识主体（然而对这种主体来说，特别的语言概念几乎不适用）。罗特曼的观点更多地是与数学有关。在所有领域的情况是，“他人的观点是公共的实体――通过主体间的一致和体现在语言中的惯例为个体主体取得意义”。忽视语言的相互交流，对于任何认知发展理论都是严重的限制。我们的认知发展大都通过语言的相互交流――多数是在儿童和他的老师之间――而发生。使教育实践建立在把语言相互作用降低为微不足道的作用的理论上，就是把它建立在其影响必定是有害的理论的基础上。皮亚杰的理论不关心个体儿童怎样在智慧上发展――或者是单独的，或者是与他人相互作用，而是关心假定的“认识主体”的发展――对这种主体来说，任何个体心灵的运算仅仅能提供一种说明。对于教育实践来说，这是一种极端古怪的基础，而教育实践不可避免地要涉及到个体儿童的发展。

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此用户未填写评价内容

评分☆☆☆☆☆

学习群论的一本非常经典的书，起点要求不高，适合自学。

评分☆☆☆☆☆

帮人买的，很好很经典的专业书。

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罗特曼是一个数学家，依据如下的事实，他的批评是特别中肯的：皮亚杰的基本模式是符合逻辑的，他经常参照集体称为“布尔巴基”的法国数学家小组。罗特曼指出，皮亚杰误解了数学的本质，特别是数学进步中证明的作用。数学的主体是一种连贯的结构，但是证明的技术不是该结构的组成部分。他说，“数学的确由证明关于结构的主张所组成。……只有对语言尤其是数学语言待贫乏作用的观点，才能支持皮亚杰提供的分析。”

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不错不错 易学易懂 适合初学者

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