The actual question is irrelevant. What I need to know is what are they actually asking me to do! I'll write the question. I can probably solve it myself. Maybe I'm just too tired to think. I will ask my prof. during seminar on Monday anyways, but I'd rather not because he would problem just solve it and I don't want that. The question is... Let N be normal in G and let f:G->H be a homomorphism whose kernel contains N. Show that f induces a homomorphism f*:G/N->H by f*(Na) = f(a). Do I only need to show that f* is well-defined and that f* is in fact a homomorphism?