Hey Lockdown.
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,.)).
Hi guys,
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 g_{i} that equals e_{G}, the corresponding word in the h_{i} must equal e_{H} (this requirement actually includes 1) above).
in short the g_{i} and the h_{i} must satisfy the same RELATIONS.