# Math Help - Proving ord(F(a)) divides order a

1. ## Proving ord(F(a)) divides order a

Allright here is a problem from one of my hw assignments and i have no idea how to solve it. Im sure there is probably a theorem or something that can be used to make it quite easy but i cant think of anything.

Let F: G->G' be a group homomorphism and suppose a is in G and a has finite order. Prove that the ord(F(a)) divides ord(a)

2. Let $x \in G$ such that $x^n = e_{G}$ where $n \in \mathbb{N}$. Since $F$ is a group homomorphism we see that $F(x^n) = F(e_G) = e_{G'}$. On the other hand $F(x^n) = (F(x))^n$. Therefore, $(F(x))^n = e_{G'}$.