Show that if $\displaystyle

f:G \to H

$ is a homomorphism, $\displaystyle

a \in G

$

and $\displaystyle

f(a)

$ has a finite order in H then

$\displaystyle

\left| a \right|

$ is infinite or $\displaystyle

\left| {f(a)} \right|

$ divides $\displaystyle

\left| a \right|

$

thank you.