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Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
If $G$ is a group such that $ (a \circ b)^i = a^i \circ b^i $ for three consecutive integers $i$, and $\space\forall a,b \in G$ , then show that $G$ is abelian. Then show this conclusion does not follow if "three" is replaced with "two".