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: Abstract Algebra Homomorphism Proof

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Let G and H be two groups. If f: G [tex]\rightarrow[/tex] H is a homomorphism, a [tex]\in[/tex] G and b = f(a). If ord(a) = n, ord(b) = m, then n is a multiple of m. (Let [tex]e_{1}[/tex] be the identity of G and [tex]e_{2}[/tex] be the identity of H)

    I have to prove that n is a multiple of m.



    2. Relevant equations
    N/A


    3. The attempt at a solution

    I know an = ?
    and that bn= ?
    then I conclude from what I get that n and m are multiples.

    Can I have some help with this proof? Thanks.
     
  2. jcsd
  3. May 2, 2010 #2
    a^n = e (in G)
    b^m = e (in H)...
     
  4. May 2, 2010 #3
    A homomorphism has what property?
     
  5. May 2, 2010 #4
    Consider these ideas:

    (1) Why is n >= m ?
    (2) With n >= m established, you can write n = q m + r, where 0 <= r < m and q > 0.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook