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More subgroups

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data

    Assume that the nonzero elements of Z13 form a group G under multiplication [a] = [ab].
    a) List the elements of the subgroup <[4]> of G, and state its order

    3. The attempt at a solution

    So I thought this would be like some of the previous problems.

    I assumed that i was simply asked to keep adding 4 and writing down the values until the value reached 0.

    The process would follow as such:

    [4] [8] [12] [3] [7] [11] [2] [6] [10] [1] [5] [9] [0]

    After placing these elements in order, I would say that the subgroup is of order 13.

    My intuition is clearly wrong, because the answer in the back of the book reads:

    {[1],[3],[4],[9],[10],[12]} o(<[4]>) = 6

    How in the world do they get this answer?
  2. jcsd
  3. Dec 7, 2008 #2


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    Science Advisor
    Homework Helper

    It says 'multiplicative subgroup'. Don't add 4. Multiply by 4.
  4. Dec 7, 2008 #3
    well... somebody feels stupid, namely me.

    Thanks for the help, buddy.
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