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
Canonical name	BurnsidePqTheorem
Date of creation	2013-03-22 13:15:58
Last modified on	2013-03-22 13:15:58
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	8
Author	yark (2760)
Entry type	Theorem
Classification	msc 20D05