The injective nature is there, but you have to show that a homomorphism exists. Can you do some re-arranging to show this? (I.e. setup phi(g1*g2) = phi(g1) . phi(g2) for (G,*) and (H,.)).
I'm wondering if the following, not a homework assignment, is true:
Let G be a group, generated by three elements, and let H be a group such that and . The map which satisfies 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?
it is not, in general, true. you need two more additional requirements:
1) for each i
2) if x is a word in the gi that equals eG, the corresponding word in the hi must equal eH (this requirement actually includes 1) above).
in short the gi and the hi must satisfy the same RELATIONS.