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. This new edition has been revised throughout, including new exercises and an additional chapter on proving that certain groups are infinite.
Read More ↓Title Statements
- Full title :Presentations of groups / D.L. Johnson.
Summary
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.
Read More ↓Edition Statements
- Publication Date:1997.
- Edition:2nd ed
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge, U.K
- Language:eng
- Publication Date:1997.
The Physical Object
- Description:1 online resource (x, 216 pages) : : illustrations
Edition Identifiers
- ISBN:9781139168410, 113916841X, 9781107089037, 1107089034, 9781107095236, 1107095239
- oclc:ocn817925523
- LC Classification:QA174
- Dewey Decimal:512/.2
Table of Contents
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 grou…
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