| 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 |
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