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


A chessboard (Fig. 7.1) has four plane symmetries, the identity e, rotation r through π about its centre, and the reflections q 1, q 2 in its two diagonals. They form a group under composition whose multiplication table is given below. It is easy to check that multiplication modulo eight makes the numbers 1, 3, 5, 7 into a group. Again we provide the corresponding table.


Symmetry Group Plane Symmetry Rotational Symmetry Equilateral Triangle Proper Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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