Presentations of groups

by Johnson, D. L.

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This revised edition provides an introduction to combinatorial group theory.

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Title Statements

Full title :Presentations of groups / D.L. Johnson.

Summary

This revised edition provides an introduction to combinatorial group theory.

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 (230 pages)

Edition Identifiers

ISBN:1316087468, 9781316087466, 1107100887, 9781107100886, 1107089034, 9781107089037, 1107095239, 9781107095236, 1107091985, 9781107091986, 9781139168410, 113916841X, 9780521585422, 0521585422
oclc:on1162435860
LC Classification:QA174
Dewey Decimal:512/.2

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…