# Fibonacci group

## Definition

The **Fibonacci group** is defined as the group with the following presentation:

where the indexes are reduced modulo .

## Particular cases

The only cases where is finite are :

Common name for | Order of group | |
---|---|---|

Trivial group | ||

Trivial group | ||

Quaternion group | ||

Cyclic group:Z5 | ||

Cyclic group:Z11 | ||

Cyclic group:Z29 |