Any finite group whose order is divisible by at most two distinct prime numbers is solvable. Proved by William Burnside using character theory, it was, before the Feit-Thompson theorem, the deepest known result on the solvability of finite groups.
Facts
StatementIf G is a finite group of order p^a q^b, where p and q are prime numbers and a and b are non-negative integers, then G is solvable. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Proved By
Source Burnside's theorem (Wikipedia)
Sources
1. Burnside's Theorem (Wikipedia)
Wikimedia FoundationHistory
The theorem was proved by William Burnside (1904) using the representation theory of finite groups.
Lead section, attribution sentence
The theorem was proved by William Burnside (1904) using the representation theory of finite groups.
View the Source Burnside's theorem (Wikipedia)
In Group: Group Theory, Lead section
G} is solvable. Hence each non-Abelian finite simple group has order divisible by at least three distinct
Proved By: William Burnside, Article text
The theorem was proved by William Burnside (1904) using the representation theory of finite groups.
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