Applications of Fibonacci numbers. Vol. 3, Proc. 3rd Int. Conf., Pisa/Italy 1988, 27-35 (1990).
[For the entire collection see Zbl 0699.00017.]
For a 2-generator group (generated by and ), the authors define the Fibonacci orbit of by , , , and the basic Fibonacci orbit of basic length by the sequence of elements of such that , , , , where is the least integer with , , for some . Also, the Fibonacci length of a generator pair (LEN) is defined by the number of elements of and the length of the basic Fibonacci orbit (BLEN) by the number of elements of . The main aim of this paper is to compute LEN and BLEN for many classical finite groups: , and ( prime number).