A set of three theorems about finite groups describing the existence, conjugacy and number of maximal p-subgroups (Sylow subgroups) for a given prime p dividing the group's order. Proved by Ludwig Sylow, they are the single most used tool for analyzing the structure of finite groups.
Facts
StatementFor every prime factor p of the order of a finite group G, there exists a Sylow p-subgroup of G of order p^n, the highest power of p dividing the order of G. Every subgroup of order p^n is a Sylow p-subgroup, all Sylow p-subgroups of G for a given prime p are conjugate to each other, and their number is congruent to 1 modulo p. 1 Classification
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Source Sylow Theorems (Wikipedia)
Proved By
Source Sylow Theorems (Wikipedia)
Sources
1. Sylow Theorems (Wikipedia)
Wikimedia FoundationStatement
The following theorems were first proposed and proven by Ludwig Sylow in 1872, and published in Mathematische Annalen.
History note on Sylow's 1872 proof
The following theorems were first proposed and proven by Ludwig Sylow in 1872, and published in Mathematische Annalen.
Principal Result Of: Ludwig Sylow, Lead sentence of the article on the result
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Peter Ludwig Sylow that give detailed information about the number of subgroups of fixed order that a given finite group contains.
In Group: Group Theory, Lead section
In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems
Proved By: Ludwig Sylow, Article text
The following theorems were first proposed and proven by Ludwig Sylow in 1872, and published in Mathematische Annalen.
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