Another type of group is called the cyclic group, which is a group generated by a single element. For example is a cyclic group because all of the elements in can be generated by by modular arithmetic. .

More formally let be a group and , is a cyclic group if ; does not mean exponentiation in that does not mean multiplied by , it means where can be addition or any defined binary operation. For example .

Another example is the group .

*Filed Under: Crashes Courses, Mathematics*

**Sources Used**

- Abstract Algebra, Theory and Application by Thomas W. Judson
- Abstract Algebra by David S. Dummit and Richard M. Foote
- Algorithms by Sanjoy Dasgupta, Christos Padadimitrou and Umesh Vazirani