1. ## Sylow's theorem

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

2. Originally Posted by dangkhoa
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 $p=q$ the group is abelian, otherwise suppose $p>q\Longrightarrow$ there exists a normal Sylow $p-$subgroup. and then $1\leq P\leq G$ is an abelian series for $G$.

Tonio