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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
  • Front/Back Matter
  • View this volume's front and back matter
    PDF
  • Chapters
  • 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
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