Burnside's theorem

In mathematics, Burnside's theorem in group theory states that if ${\displaystyle G}$ is a finite group of order ${\displaystyle p^{a}q^{b}}$ where ${\displaystyle p}$ and ${\displaystyle q}$ are prime numbers, and ${\displaystyle a}$ and ${\displaystyle b}$ are non-negative integers, then ${\displaystyle G}$ is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct primes.