# Math Help - Homomorphic Image Question

1. ## Homomorphic Image Question

Suppose that the group (H,#) is a homomorphic image of the group (G,*). Is (G,*) necessarily a homomorphic image of the group (H,#)?

2. No! $H$ could be smaller than $G$, and then there is no way $G$ could be the image of any kind of function defined on $H$.