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Homework Help: Counting the number of homorphisms

  1. Aug 7, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi,
    I am trying to solve the following question:
    count the number of homomorphism between Z/mZ and Z/nZ?
    Can you tell me is my solution correct?


    2. Relevant equations



    3. The attempt at a solution
    Let f be a homorphism.
    f(mZ + a) = nZ + b ; a,b belong to G
    Now, o(nZ+b) | n (from lagrangian theorem)
    o(f(mZ+a)) = o(nZ+b); and o(f(mZ+a)) | o(mZ+a) which implies o(nZ+b) | m
    Number of possiblities for o(nZ+b) = Number of common factors for m and n = Eulers Quotient for gcd(m,n)

    Can you tell me if the approach correct? Because when i check the answers of the exercise question it is gcd(m,n) but here i am getting Euler's Qutient for gcd(m.n) = [tex]\varphi(gcd(m,n))[/tex]

    Thanks,
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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