# Burnside $p$-$q$ theorem

Any group whose order is divisible by only two distinct primes is solvable. (These two distinct primes are the $p$ and $q$ of the title.)

It follows that if $G$ is a non-abelian finite simple group, then $|G|$ must have at least three distinct prime divisors.

Title Burnside $p$-$q$ theorem BurnsidePqTheorem 2013-03-22 13:15:58 2013-03-22 13:15:58 yark (2760) yark (2760) 8 yark (2760) Theorem msc 20D05