section_path: Abstract algebra/Group theory
section_name: Group theory
paragraph_text: Group theory
  
  In the theory of finite groups the Sylow theorems imply that, if a power of a prime number p n {\displaystyle p^{n}} divides the order of a group, then the group has a subgroup of order p n {\displaystyle p^{n}}. By Lagrange's theorem, any group of prime order is a cyclic group,and by Burnside's theorem any group whose order is divisible by only two primes is solvable.