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Presentations of groups /
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. T...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, U.K. ; New York, NY, USA :
Cambridge University Press,
1997.
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| Edición: | 2nd ed. |
| Colección: | London Mathematical Society student texts ;
15. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Dedication; CONTENTS; PREFACE TO THE SECOND EDITION; CHAPTER 1 FREE GROUPS; 1. Definition and elementary properties; 1.1 Definition and elementary properties; 2. Existence of F(X); 1.2 Existence of F(X); 1.3 Further properties of F(X); 3. Further properties of F(X); 1.3 Further properties of F(X); Exercises; CHAPTER 2 SCHREIER'S METHOD; 1. The well-ordering of F; 2.1 The well-ordering of F; 2. The Schreier transversal; 2.2 The Schreier transversal; 3. The Schreier generators; 4. Decomposition of the set A; 5. Freeness of the generators B; 6. Conclusion; Exercises
- CHAPTER 3 NIELSEN'S METHOD1. The finitely-generated case; 2. Example 1; 3. The general case; 4. Further applications; Exercises; CHAPTER 4 FREE PRESENTATIONS OF GROUPS; 1. Basic concepts; 2. Induced homomorphisms; 3. Direct products; 4. Tietze transformations; 5. van Kampen diagrams; Exercises; CHAPTER 5 SOME POPULAR GROUPS; 1. The quaternions; 2. The Heisenberg group; 3. Symmetric groups; 4. Semi-direct products; 5. Groups of symmetries; 6. Polynomials under substitution; 7. The rational numbers; Exercises; CHAPTER 6 FINITELY-GENERATED ABELIAN GROUPS; 1. Groups-made-abelian
- 2. Free abelian groups3. Change of generators; 4. The invariant factor theorem for matrices; 5. The basis theorem; Exercises; CHAPTER 7 FINITE GROUPS WITH FEW RELATIONS; 1. Metacyclic groups; 2. Interesting groups with three generators; 3. Cyclically-presented groups; Exercises; CHAPTER 8 COSET ENUMERATION; 1. The basic method; 2. A refinement; Exercises; CHAPTER 9 PRESENTATIONS OF SUBGROUPS; 1. The method; 2. Alternating groups; 3. Braid groups; 4. von Dyck groups; 5. Triangle groups; 6. Free products; 7. HNN-extensions; 8. The Schur multiplicator; Exercises
- CHAPTER 10 PRESENTATIONS OF GROUP ExTENSIONS1. Basic concepts; 2. The main theorem; 3. Special cases; (S) Semi-direct products; (A) Extensions with abelian kernel; (Z) Central extensions; (D) The direct product; 4. Finite p-groups; Exercises; CHAPTER 11 RELATION MODULES; 1. G-modules; 2. The augmentation ideal; 3. Derivations; 4. Free differential calculus; 5. The fundamental isomorphism; Exercises; CHAPTER 12 AN ALGORITHM FOR N/N'; 1. The Jacobian; 2. The proof; 3. Examples; Exercises; CHAPTER 13 FINITE p-GROUPS; 1. Review of elementary properties; 2. Power-commutator presentations
- 3. mod p modulesExercises; CHAPTER 14 THE NILPOTENT QUOTIENT ALGORITHM; 1. The algorithm; 2. An example; 3. An improvement; Exercises; CHAPTER 15 THE GOLOD-SHAFAREVICH THEOREM; 1. The proof; 2. An example; 3. Related results; Exercises; CHAPTER 16 PROVING SOME GROUPS INFINITE; 1. Dimension subgroups; 2. The Gaschiitz-Newman formulae; 3. Newman's criterion; 4. Fibonacci update; Exercises; Guide to the literature and references; INDEX; Dramatis Personae