《群論導論（第4版）（英文版）》介紹了：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
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圖書目錄
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
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