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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

    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.
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