(adsbygoogle = window.adsbygoogle || []).push({}); 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 a^{n}= ?

and that b^{n}= ?

then I conclude from what I get that n and m are multiples.

Can I have some help with this proof? Thanks.

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# Homework Help: Abstract Algebra Homomorphism Proof

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