Let G be a group of order pq where p and q are distinct primes. Prove
that G is soluble.
Can you give me some instructions on this question by using Sylow's theorem please?
Many thanks
If $\displaystyle p=q$ the group is abelian, otherwise suppose $\displaystyle p>q\Longrightarrow$ there exists a normal Sylow $\displaystyle p-$subgroup. and then $\displaystyle 1\leq P\leq G$ is an abelian series for $\displaystyle G$.