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Solution

Reason: From (xy)² = xyxy = x²y² = xxyy. Left-multiply by x⁻¹ and right-multiply by y⁻¹ to get yx = xy, hence G is abelian. (2) and (3) are false (there exist non-abelian groups where every element has order 3 or 5, e.g., unitriangular 3×3 matrices over ℤ₃/ℤ₅). (4) is false because every subgroup of an abelian (commutative) group is abelian.