Fibonacci group

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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