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Noncommutative group with twelve elements.

  1. Oct 22, 2008 #1
    1. The problem statement, all variables and given/known data

    I need to find a group with twelve elements that is noncommutative.


    2. Relevant equations



    3. The attempt at a solution

    I was considering a group G of the integers (-5,-4,-3,-2-,-1,0,1,2,3,4,5) with respect to subtraction. Subtraction is associative/noncommutative, G has the neutral element, and every element has an inverse! Excellent!

    But (!) it composes only eleven elements! I need twelve!
     
  2. jcsd
  3. Oct 22, 2008 #2

    CompuChip

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    Also, it is not a group.
    3 - (-3) is not an element of your set.
    0 is not a left identity element either: 0 - 3 is not 3.

    Try thinking about geometric groups (symmetries of 2 and 3-dimensional objects).
     
  4. Oct 22, 2008 #3

    Dick

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    (1-2)-3=1-(2-3)??? Subtraction isn't associative either. Subtraction is a pretty poor candidate for a group operation.
     
  5. Oct 22, 2008 #4
    Thank you CompuChip! :)
     
  6. Oct 22, 2008 #5

    CompuChip

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    And Dick :smile:

    Did you solve it now?
     
  7. Oct 22, 2008 #6
    At least I think I did. :) I regarded the geometrical figure with six edges. And looked at the mirroring and rotations of that structure. Is that better?
     
  8. Oct 22, 2008 #7

    Dick

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    That works fine.
     
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