Fibonacci group

Definition

The Fibonacci group $F(2,m)$ is defined as the group with the following presentation:

$\{ x_1, x_2, \dots, x_m | x_ix_{i+1} = x_{i+2}\}$

where the indexes are reduced modulo $m$.

Particular cases

The only cases where $F(2,m)$ is finite are $m = 1,2,3,4,5,7$:

$m$	Common name for $F(2,m)$	Order of group
$1$	Trivial group	$1$
$2$	Trivial group	$1$
$3$	Quaternion group	$8 = 2^3$
$4$	Cyclic group:Z5	$5$
$5$	Cyclic group:Z11	$11$
$7$	Cyclic group:Z29	$29$

External links

• Springer Online Reference page