Topics in the Theory of Group Presentations

D. L. Johnson

doi:10.1017/CBO9780511629303

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 have been added and the treatment of a number of topics has been improved and expanded. In addition, there are new chapters on the triangle groups, small cancellation theory and groups from topology. The connections between the theory of group presentations and other areas of mathematics are emphasized throughout. The book can be used as a text for beginning research students and, for specialists in other fields, serves as an introduction both to the subject and to more advanced treatises.

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Topics in the Theory of Group Presentations

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Chapter I - Free groups and free presentations
pp 1-41

Chapter II - Examples of presentations
pp 42-61

Chapter III - Groups with few relations
pp 62-84

Chapter IV - Presentations of subgroups
pp 85-129

Chapter V - The triangle groups
pp 130-146

Chapter VI - Extensions of groups
pp 147-211

Chapter VII - Small cancellation groups
pp 212-244

Chapter VIII - Groups from topology
pp 245-290

Guide to the literature and references
pp 291-300

Index of notation
pp 301-306

Index
pp 307-311

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