Hi guys,

I'm wondering if the following, not a homework assignment, is true:

Let G be a group, generated by three elements, $\displaystyle G= \langle g_1, g_2 , g_3 \rangle$ and let H be a group such that $\displaystyle |H|=|G|$ and $\displaystyle H=\langle h_1,h_2,h_3 \rangle$. The map $\displaystyle \phi : G\to H$ which satisfies $\displaystyle \phi(g_i)=h_i$ for i=1,2,3 is an isomorphism.

It is a sort of lemma I wish to be true in order to prove something else.

Can anyone help?