Sylow p-subgroup | Sylow theorems

If p^k is the highest power of a prime p dividing the order of a finite group G, then a subgroup of G of order p^k is called a Sylow p-subgroup of G.

Let p be a prime number, G a finite group, and left bracketing bar G right bracketing bar the order of G. 1. If p divides left bracketing bar G right bracketing bar , then G has a Sylow p-subgroup. 2. In a finite group, all the Sylow p-subgroups are conjugate for some fixed p. 3. The number of Sylow p-subgroups for a fixed p is congruent to 1 (mod p).

Abhyankar's conjecture | subgroup | Sylow theorems

conjugate subgroup | Sylow p-subgroup

Peter Ludwig Mejdell Sylow

Peter Ludwig Mejdell Sylow

Sylow p-subgroup | Sylow theorems