• M. A. Armstrong
Part of the Undergraduate Texts in Mathematics book series (UTM)


Without further ado we define the notion of a group, using the symmetries of the tetrahedron as guide. The first ingredient is a set. The second is a rule which allows us to combine any ordered pair x, y of elements from the set and obtain a unique “product” xy which also lies in the set. This rule is usually referred to as a “multiplication” on the given set.


Matrix Multiplication Identity Element Benzene Molecule Word Product Regular Tetrahedron 


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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • M. A. Armstrong
    • 1
  1. 1.Department of Mathematical SciencesUniversity of DurhamDurhamEngland

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