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D = {(g, g) : g is in G}. Prove that D is normal in GxG if andonly if G is Abelian.

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Let G be a group. Let G′ be the collection of all products in G of the form a1i1a2i2 ···akik where each aj itself has the form x−1y−1xy, each ij = ±1, and k is any positive integer.

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Prove that H is a normal subgroup of G

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