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#### TheBigBadBen

##### Active member

- May 12, 2013

- 84

If there is an epimorphism (i.e. onto homomorphism) $\phi:G\times G \to H\times H$, is there necessarily an epimorphism $\psi:G\to H$? If not, under what conditions can we ascertain such an epimorphism given the existence of $\phi$?

I would think that this is true for abelian groups $G$ and $H$ by their respective decompositions, but I'm not sure how I'd show that to be the case. Also, I don't have a good guess for the general case. It seems clear that the isomorphism theorem should play a role at some point, but that doesn't lead to any obvious conclusions.