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Homework Help: Group theory

  1. Jan 19, 2008 #1
    [SOLVED] group theory

    1. The problem statement, all variables and given/known data
    My book says that Z_3 cross Z_4 is isomorphic to Z_12, which I am confused about because
    Z_3 cross Z_4 has four different generators and Z_12 only has 1.

    EDIT: wait that is not true, Z_12 has generators 1,5,7,11
    It is probably true in general that the number of generators of Z_n is equal to phi(n) where phi is the Euler phi function.
    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jan 19, 2008
  2. jcsd
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