High Quality Content by WIKIPEDIA articles! In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow. The three main Sylow theorems are the Sylow E theorem, the Sylow D theorem, and the Sylow C theorem, sometimes referring to the "existence", "development" and "conjugate" theorem respectively. Another theorem gives the number of Sylow p-subgroups of a group for fixed prime p; this is sometimes referred to as the Sylow "counting" theorem. Given any prime number and any finite group, the Sylow E theorem asserts the existence of a subgroup of this finite group, having order the power of this prime. The Sylow D theorem asserts the equivalence between maximality of a p-subgroup of a finite group, and that it is a Sylow subgroup of the group. Finally, the Sylow C theorem asserts that all Sylow p-subgroups of a group (for fixed prime p) are conjugate to each other.