Choose the correct statement for a group G:
Pick an option to check yourself, or open the answer below.
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Correct answer: A. If for all x, y ∈ G, (xy)² = x²y², then G is commutative.
Explanation
(xy)² = x²y² means xyxy = xxyy; cancelling x on the left and y on the right gives yx = xy, so G is abelian. Groups of exponent 3 or 5 need not be abelian (e.g. the Heisenberg group mod 3 has every element of order 3 and is non-abelian). Every subgroup of an abelian group is abelian, so D is false.More Discrete Structures and Optimisation questions
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