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The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
Table of contents:
1. Free groups; 2. Schreier's method; 3. Nielsen's method; 4. Free presentations of groups; 5. Some popular groups; 6. Finitely generated groups; 7. Finite groups with few relations; 8. Coset enumeration; 9. Presentations of subgroups; 10. Presentations of group extensions; 11. Relation models; 12. An algorithm for N/N'; 13. Finite p-groups; 14. The nilpotent quotient algorithm; 15. The Golod-Shafarevich theorem; 16. Fibonacci update.
The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
This revised edition provides an introduction to combinatorial group theory.
Table of contents:
1. Free groups; 2. Schreier's method; 3. Nielsen's method; 4. Free presentations of groups; 5. Some popular groups; 6. Finitely generated groups; 7. Finite groups with few relations; 8. Coset enumeration; 9. Presentations of subgroups; 10. Presentations of group extensions; 11. Relation models; 12. An algorithm for N/N'; 13. Finite p-groups; 14. The nilpotent quotient algorithm; 15. The Golod-Shafarevich theorem; 16. Fibonacci update.
The aim of this book is to provide an introduction to combinatorial group theory. Any reader who has completed first courses in linear algebra, group theory and ring theory will find this book accessible. The emphasis is on computational techniques but rigorous proofs of all theorems are supplied. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
This revised edition provides an introduction to combinatorial group theory.