Problem 3
If $G$ is a group in which $(ab) ^i = a^i b^i$ for three consecutive integers $i$, prove that $G$ is abelian.
Show that the result of problem 3 would not always be true if the word “three“ were replaced by “two”. in other words, show that there is a group $G$ and consecutive numbers $i$, $i +1$ such that $G$ is not abelian but does have the property that
$$(ab) ^i = a^i b^i$$ and
$$(ab)^{i+1} = a^{i+1} b^{i+1}$$
$\forall \, a, b \in G$
