Assume $G = \{1,a,b,c\}$ is a group of order 4 with identity $1$. Assume also that $G$ has no elements of order $4$ (so the order must be $\leq 3$). Use the cancellation laws to show that there is a unique group table for $G$. Deduce that $G$ is abelian.
Although it was more about clarifying the wording of the problem than about the problem itself.
Linear & Abstract algebra
Linear & Abstract algebra