Groups and Their Graphs

Israel Grossman; Wilhelm Magnus

doi:10.5948/UPO9780883859292

The abstract nature of group theory makes its exposition, at an elementary level, difficult. The authors of the present volume have overcome this obstacle by leading the reader slowly from the concrete to the abstract, from the simple to the complex, employing effectively graphs or Cayley diagrams to hlep the student visualize some of the structural properties of groups. Among the concrete examples of groups, the authors include groups of congruence motions and groups of permutations. A conscientious reader will acquire a good intuitive grasp of this pwerful subject.

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Groups and Their Graphs

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp 1-2

Chapter 1 - Introduction to Groups
pp 3-9

Chapter 2 - Group Axioms
pp 10-14

Chapter 3 - Examples of Groups
pp 15-25

Chapter 4 - Multiplication Table of a Group
pp 26-40

Chapter 5 - Generators of a Group
pp 41-43

Chapter 6 - Graph of a Group
pp 44-55

Chapter 7 - Definition of a Group by Generators and Relations
pp 56-76

Chapter 8 - Subgroups
pp 77-88

Chapter 9 - Mappings
pp 89-106

Chapter 10 - Permutation Groups
pp 107-119

Chapter 11 - Normal Subgroups
pp 120-136

Chapter 12 - The Quaternion Group
pp 137-140

Chapter 13 - Symmetric and Alternating Groups
pp 141-149

Chapter 14 - Path Groups
pp 150-159

Chapter 15 - Groups and Wallpaper Designs
pp 160-166

Appendix: Group of the Dodecahedron and the Icosahedron
pp 167-169

Solutions
pp 170-188

Bibliography
pp 189-191

Index
pp 192-195

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