Problem 10

Let $G$ be a finite group with order $m$.

1. State the smallest value of $m$ such that $G$ is non-abelian.

2. Prove that the value of $m$ found in (a) is the smallest value that allows $G$ to be non-abelian.

3. Hence prove that for all even integers $n\geq m$, there exists a non-abelian group of order $n$.