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Anneli Lax New Mathematical Library
Groups and Their Graphs
Digital content for Groups and Their Graphs
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 help 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 powerful subject.
Table Of Contents
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Front/Back Matter
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View this volume's front and back matter
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Chapters
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Chapter 1. Introduction to Groupspp. 3 - 9
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Chapter 2. Group Axiomspp. 10 - 14
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Chapter 3. Examples of Groupspp. 15 - 25
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Chapter 4. Multiplication Table of a Grouppp. 26 - 40
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Chapter 5. Generators of a Grouppp. 41 - 43
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Chapter 6. Graph of a Grouppp. 44 - 55
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Chapter 7. Definition of a Group by Generators and Relationspp. 56 - 76
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Chapter 8. Subgroupspp. 77 - 88
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Chapter 9. Mappingspp. 89 - 106
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Chapter 10. Permutation Groupspp. 107 - 119
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Chapter 11. Normal Subgroupspp. 120 - 136
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Chapter 12. The Quaternion Grouppp. 137 - 140
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Chapter 13. Symmetric and Alternating Groupspp. 141 - 149
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Chapter 14. Path Groupspp. 150 - 159
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Chapter 15. Groups and Wallpaper Designspp. 160 - 166
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Appendix. Group of the Dodecahedron and the Icosahedronpp. 167 - 169
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