1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted