2 First Isomorphism Theorem. Let G be a group and H = {(9,9)|g E G) (a)...

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2 First Isomorphism Theorem. Let G be a group and H = {(9,9)|g E G) (a) Prove that H is a subgroup of Gx G. (b) JTSbow that the following conditions are equivalent (i) G in abelian. () H in a normal subgroup of Gx G. (e) Suppose G abelian and show that (G x G)/HG. 2 First Isomorphism Theorem. Let G be a group and H = {(9,9)|g E G) (a) Prove that H is a subgroup of Gx G. (b) JTSbow that the following conditions are equivalent (i) G in abelian. () H in a normal subgroup of Gx G. (e) Suppose G abelian and show that (G x G)/HG.