##  [Cyclic Group](/cyclic-group) 

  ##  [Cyclic Group](https://algebra.quantumdictionary.io/cyclic-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 generated by a single element g: G = = {g^n : n in Z} for infinite cyclic or {g^n : n in Z_n} for finite cyclic groups. Every element of G is a power (or integer multiple, in additive notation) of the generator.