For G and H groups, show that (G×{e})◃(G×H), then show that the quotient (G×H)/(G×{e}) is isomorphic to H.

Question

Have no idea where to start :( I think the solution will have to be something like showing that the group (G x {e}) is normal by doing something with left cosets, and isomorphism wouldn't be too hard to check after that part, but I'm really stuck

Answer 1

Consider the map from $G\times H$ to $H$ given by $(g,h)\mapsto h$. Prove it's a group homomorphism; then note that its kernel is $G\times\{e\}$; then use the theorems that say the kernel of a group homomorphism is a normal subgroup, and the image is isomorphic to the quotient.