##  [Simple Group](/simple-group) 

  ##  [Simple Group](https://algebra.quantumdictionary.io/simple-group-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 nontrivial group whose only normal subgroups are the trivial subgroup and the group itself. Equivalently, it has no nontrivial proper normal subgroups; simple groups are the indecomposable building blocks in the sense of composition series.