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Complete the group as isomorphic

  1. Dec 9, 2007 #1
    1. Complete the following table to obtain a Group, G, that is isomorphic to Z4
    2. Complete the same table to obtain a Group, H, that is NOT isomorphic to Z4

    *| a b c d


    I tried to complete the group as isomorphic, can anyone tell me if this is correct?

    *| a b c d

    a| a a a a
    b| a b c d
    c| a c a c
    d| a d c b

    And here is my attempt at part to as if it is not an isomorphism

    *| a b c d

    a| a b c d
    b| b c d a
    c| c d a b
    d| d a b c
    Last edited: Dec 9, 2007
  2. jcsd
  3. Dec 9, 2007 #2


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    Staff Emeritus
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    Gold Member

    You're saying that this is the multiplication table for a group? What's the inverse of b?
  4. Dec 9, 2007 #3

    All I can say is LOL you might wanna work on the table with all a's in it. It has to follow group properties. I hope that's not the grade you want in this class.
  5. Dec 9, 2007 #4
    ok here

    ok now that you got rid of all those crazy a's here is what I got.

    Part 1. isomorphic to Z4

    part 2. not isomorphic to Z4

    Anyone else get this?
  6. Dec 9, 2007 #5
    Thanks, I was talking it over with some friends and we all got the same thing. Thanks for the assistance haha now I can definatly get an A ^_^
  7. Dec 10, 2007 #6


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    Staff Emeritus
    Science Advisor

    Yes, all groups of order 4 are either isomorphic to Z4 or the Klein 4 group.

    CrazyCalcGirl- please do NOT give complete answers in the homework section.
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