##  [Normal Subgroup](/normal-subgroup) 

  ##  [Normal Subgroup](https://algebra.quantumdictionary.io/normal-subgroup-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 subgroup N of a group G such that for every g in G and n in N, the conjugate gng^{-1} lies in N; equivalently, left cosets equal right cosets and N is invariant under conjugation by G.