##  [Feit–Thompson Theorem](/feit-thompson-theorem) 

  ##  [Feit–Thompson Theorem](https://algebra.quantumdictionary.io/feit-thompson-theorem-0) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A landmark theorem in finite group theory: every finite group of odd order is solvable. In particular, there are no nonabelian simple finite groups whose order is odd. The proof is long and uses deep representation-theoretic and local analysis, and the statement is a major structural restriction on finite simple groups.