Let G1 and G2 be groups. It is a fact that (G1 x G2 )/( G1 x {e2}) is isomorphic to G2 a) Given how factor groups work, give an intuitive reason why this is so. D) You will now show that the isomorphism holds using the Fundamental Homomorphism Theorem. To do so you need to define a function 6: G x G2 - G2 that satisfies the following: • phi is a homomorphism. • phi is onto • ker ø = G1 x {e2}.

Let G1 and G2 be groups. It is a fact that (G1 x G2 )/( G1 x {e2}) is isomorphic to G2 a) Given how factor groups work, give an intuitive reason why this is so. D) You will now show that the isomorphism holds using the Fundamental Homomorphism Theorem. To do so you need to define a function 6: G x G2 - G2 that satisfies the following: • phi is a homomorphism. • phi is onto • ker ø = G1 x {e2}.