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Homework Help: Isomorphisms problem homework

  1. Oct 3, 2007 #1
    1. The problem statement, all variables and given/known data

    Prove or disprove U(20) and U(24) are isomorphic

    2. Relevant equations



    3. The attempt at a solution

    U(20)={1,3,,7,9,11,13,17,19}
    U(24)={1,5,7,11,13,17,19}

    In U(20), Order(1)=1 Order(3)=4 Order(7)=4 Order(9)=2, Order(11)=2 Order(13)=4, Order(17)=4, Order(19)=2

    In U(24), Order(1)= 1 , Order(5)=2 , ORder(7)=2, Order(11)=2 , Order(13)=2 , Order(17)=2, Order(19)= 2

    Since each of the elements in each of the groups do not generate the same order for each elements in the opposite group, can't I conclude thatt U(24) and U(20) are not isomorphic?
     
  2. jcsd
  3. Oct 3, 2007 #2

    morphism

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    Science Advisor
    Homework Helper

    You can say that U(24) has 6 elements of order 2, while U(20) doesn't. So they certainly can't be isomorphic.

    (By the way, you're missing 23 in U(24). So in fact U(24) has 7 elements of order 2, but this is immaterial.)
     
    Last edited: Oct 3, 2007
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