| 词条 | 群论导论 |
| 释义 | 图书信息出版社: 世界图书出版公司; 第1版 (2009年8月1日) 外文书名: An Introduction to the Theory of Groups 平装: 513页 正文语种: 英语 开本: 24 ISBN: 7510004985, 9787510004988 条形码: 9787510004988 尺寸: 22.2 x 14.8 x 2.2 cm 重量: 640 g 作者简介作者：(美国)罗曼(Joseph J.Rotman) 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 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 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 Burnside's 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 Tietze's 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 Boone's Lemma Cancellation Diagrams The Novikov-Boone-Britton Theorem: Necessity of Boone's 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 Zorn's Lemma APPENDIX V Countability APPENDIX VI Commutative Rings Bibliography Notation Index |
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