##  [Finite Group](/finite-group) 

  ##  [Finite Group](https://algebra.quantumdictionary.io/finite-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 group whose underlying set has finite cardinality |G| = n for some natural number n. The order of the group is the number of its elements; many theorems in group theory specialize to the finite case and exploit counting arguments.