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Topics in the theory of group presentations /
These notes comprise an introduction to combinatorial group theory and represent an extensive revision of the author's earlier book in this series, which arose from lectures to final-year undergraduates and first-year graduates at the University of Nottingham. Many new examples and exercises ha...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [England] ; New York :
Cambridge University Press,
1980.
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| Colección: | London Mathematical Society lecture note series ;
42. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; Chapter I. Free groups and free presentations; 1. Elementary properties of free groups; 2. The Nielsen-Schreier theorem; 3. Free presentations of groups; 4. Elementary properties of presentations; Chapter II. Examples of presentations; 5. Some popular groups; 6. Finitely-generated abelian groups; Chapter III. Groups with few relations; 7. Metacyclic groups; 8. Interesting groups with three generators; 9. Cyclically-presented groups; Chapter IV. Presentations of subgroups; 10. A special case; 11. Coset enumeration
- 12. The Reidemeister-Schreier rewriting process13. A method for presenting subgroups; Chapter V. The triangle groups; 14. The Euclidian case; 15. The elliptic case; 16. The hyperbolic case; Chapter VI. Extensions of groups; 17. Extension theory; 18. Teach yourself cohomology of groups; 19. Local cohomology and p-groups; 20. Presentations of group extensions; 21. The Golod-Safarevic theorem; 22. Some minimal presentations; Chapter VII. Small cancellation groups; 23. van Kampen diagrams; 24. From Eulerfs formula to Dehn's algorithm; 25. The existence of non-cyclic free subgroups
- 26. Some infinite Fibonacci groupsChapter VIII. Groups from topology; 27. Surfaces; 28. Knots; 29. Braids; 30. Tangles; Guide to the literature and references; Index of notation; Index