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Sylow Theorems

Result

Sylow p-subgroup | Sylow theorems

Definitions

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).

conjugate subgroup | Sylow p-subgroup

Associated people

Peter Ludwig Mejdell Sylow

Scientific contributions

Sylow p-subgroup | Sylow theorems

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