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Generating Sets

  1. Jan 29, 2010 #1
    1. The problem statement, all variables and given/known data
    List the elements of the subgroup generated by the given subset:

    The subsets {4,6} of Z12


    2. Relevant equations



    3. The attempt at a solution

    so the GCD of 4 and 12 is 4, 12/4 = 3 elements that <4> generates : {0, 4, 8}
    GCD of 6 and 12 is 6, 12/6 = 2 elements that <6> generates : {0, 6}
    {4+6} = {10} GCD of 12 and 10 is 2, 12/2 = 6 elements 10 generates : {0, 2, 4, 6, 8, 10}

    so {4,6} generates the subgroup {0,2,4,6,8,10} right?
     
  2. jcsd
  3. Jan 29, 2010 #2
    Looks fine to me.
     
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