(3) Let G be a group with identity ej and let G, be a group with identity en Consider the set of ordered pairs G G2 = {(

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3 Let G Be A Group With Identity Ej And Let G Be A Group With Identity En Consider The Set Of Ordered Pairs G G2 1 (12.88 KiB) Viewed 23 times

(3) Let G be a group with identity ej and let G, be a group with identity en Consider the set of ordered pairs G G2 = {(1.12): G and 12 € Ga). Define multiplication on GGz as follows: (1r).wa) = (v2). (a) Prove that this multiplication is associative, (b) Prove that .cy) is a multiplicative identity (c) Prove that (119) = (''). (d) Prove that if G and G, are abelian groups, then the multiplication in GXGin commutative.