Suppose that the group (H,#) is a homomorphic image of the group (G,*). Is (G,*) necessarily a homomorphic image of the group (H,#)?
Follow Math Help Forum on Facebook and Google+
No! $\displaystyle H$ could be smaller than $\displaystyle G$, and then there is no way $\displaystyle G$ could be the image of any kind of function defined on $\displaystyle H$.
View Tag Cloud