Presentations of Groups

D. L. Johnson

doi:10.1017/CBO9781139168410

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.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-x
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Preface
pp xi-xii
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1 - Free Groups
pp 1-13
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2 - Schreier's Method
pp 14-25
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3 - Nielsen's Method
pp 26-40
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4 - Free Presentations of Groups
pp 41-57
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5 - Some Popular Groups
pp 58-73
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6 - Finitely-generated Abelian Groups
pp 74-86
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7 - Finite Groups with few Relations
pp 87-99
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8 - Coset Enumeration
pp 100-115
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9 - Presentations of Subgroups
pp 116-135
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10 - Presentations of Group Extensions
pp 136-145
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11 - Relation Modules
pp 146-159
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12 - An Algorithm for N/N′
pp 160-167
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13 - Finite p-groups
pp 168-177
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14 - The Nilpotent Quotient Algorithm
pp 178-185
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15 - The Golod-Shafarevich Theorem
pp 186-190
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16 - Proving some Groups Infinite
pp 191-200
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Guide to the literature and references
pp 201-210
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Index
pp 211-214
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Dramatis personae
pp 215-216
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Presentations of Groups

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Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xii

1 - Free Groups
pp 1-13

2 - Schreier's Method
pp 14-25

3 - Nielsen's Method
pp 26-40

4 - Free Presentations of Groups
pp 41-57

5 - Some Popular Groups
pp 58-73

6 - Finitely-generated Abelian Groups
pp 74-86

7 - Finite Groups with few Relations
pp 87-99

8 - Coset Enumeration
pp 100-115

9 - Presentations of Subgroups
pp 116-135

10 - Presentations of Group Extensions
pp 136-145

11 - Relation Modules
pp 146-159

12 - An Algorithm for N/N′
pp 160-167

13 - Finite p-groups
pp 168-177

14 - The Nilpotent Quotient Algorithm
pp 178-185

15 - The Golod-Shafarevich Theorem
pp 186-190

16 - Proving some Groups Infinite
pp 191-200

Guide to the literature and references
pp 201-210

Index
pp 211-214

Dramatis personae
pp 215-216

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