##  [Maschke's Theorem](/maschkes-theorem) 

  ##  [Maschke's Theorem](https://puremath.quantumdictionary.io/maschkes-theorem-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A criterion in representation theory stating that for a finite group G and a field k whose characteristic does not divide |G|, the group algebra k[G] is semisimple; equivalently every finite-dimensional k-representation of G decomposes as a direct sum of irreducible representations.

 

 

 

 

 





 

 



 ##  [Maschke's Theorem](https://algebra.quantumdictionary.io/maschkes-theorem-1) 

  

 [![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 criterion for complete reducibility of representations of a finite group G over a field k: the group algebra kG is semisimple (equivalently every finite-dimensional representation is completely reducible) precisely when the characteristic of k does not divide the order of G.