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Homework Help: Subgroups of External Direct Products

  1. Apr 9, 2006 #1
    Problem "Find all subgroups of order 3 in Z9 x Z3"

    Using an external direct product I came out with the elements:

    0,0
    0,1
    0,2
    0... to 0,9
    1,0
    1.... to 1,9
    2,0
    2.... to 2,9


    With subgroups:

    {(0,0),(1,0),(2,0)}
    {(0,0),(0,3),(0,6)}
    {(0,0),(1,3),(2,6)}
    {(0,0),(1,6),(2,3)}

    Just looking for some confirmation if I have done this correctly. I was reading my book and it was lacking a definition/example that I felt like I fully understood.
     
  2. jcsd
  3. Apr 9, 2006 #2

    AKG

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    Science Advisor
    Homework Helper

    This is 99% correct, it's just that you've given subgroups of Z3 x Z9, not Z9 x Z3.
     
  4. Apr 9, 2006 #3
    Wow... nice catch. Now I'm wondering if I can just write on top of the page to switch everything to the other side or if I should re-write the page :(.

    I'll just write a little snippet about it and then re-write the subgroups. That seems to the best way about fixing this. Thanks for the help.
     
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