Editing Prime number (section)

=== Group theory ===
In the theory of [[finite group]]s the [[Sylow theorems]] imply that, if a power of a prime number <math>p^n</math> divides the [[order of a group]], then the group has a subgroup of order {{tmath|p^n}}. By [[Lagrange's theorem (group theory)|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 group|solvable]].<ref>{{cite book|title=The Theory of Groups|series=Dover Books on Mathematics|first=Marshall|last=Hall|author-link=Marshall Hall (mathematician)|publisher=Courier Dover Publications|year=2018|isbn=978-0-486-81690-6|url=https://books.google.com/books?id=K8hEDwAAQBAJ}} For the Sylow theorems see p. 43; for Lagrange's theorem, see p. 12; for Burnside's theorem see p. 143.</ref>