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Group theory

  1. Apr 29, 2014 #1
    Can one set up a multiplication table for the symmetry group C3V of the equilateral
    triangle.
    Then show that it is identical to that of the permutation group P3.

    I need some clarification....


    What about a matrix representation (2x2) for these groups?
    → Here was thinking to use Cartesian coordinate
    system in the xy plane, with origin at the center of the triangle.
     
  2. jcsd
  3. Apr 29, 2014 #2

    Zondrina

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    Homework Helper

    I believe this will help answer your question about the symmetry group of the equilateral triangle:

    http://dogschool.tripod.com/trianglegroup.html

    The symmetry group of the equilateral triangle is indeed isomorphic to the dihedral group of order six (degree three) ##D_3##.

    It is also isomorphic to ##SL(2, 2)## I believe.
     
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