# Homework Help: Abstract Algebra Homomorphism Proof

1. May 2, 2010

### The_Iceflash

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

Let G and H be two groups. If f: G $$\rightarrow$$ H is a homomorphism, a $$\in$$ G and b = f(a). If ord(a) = n, ord(b) = m, then n is a multiple of m. (Let $$e_{1}$$ be the identity of G and $$e_{2}$$ 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. May 2, 2010

### The Chaz

a^n = e (in G)
b^m = e (in H)...

3. May 2, 2010

### Tedjn

A homomorphism has what property?

4. May 2, 2010

### gauss^2

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.