Consider maps π1 : G1 × G2 → G1 given by π1(g1, g2) = g1 and π2 : G1 × G2 → G2 given by π2(g1, g2) = g2.  Show that π1 and π2 are homomorphisms (You can just show one of them is a homomorphism and say the other one follows similarly.)

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