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(w_n)_n_³₀ is a non-degenerate Lucas sequence with real roots, then there are only finitely many non-abelian finite simple groups whose order is a member of _n_³₀. For the particular case of the classical Fibonacci and Lucas sequences, there is no such non-abelian finite simple group.

JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 1, Pages 23 - 54 (April 2004)

FIBONACCI NUMBERS, LUCAS NUMBERS AND ORDERS OF FINITE SIMPLE GROUPS
Florian Luca (Mexico)

Abstract:
In this paper, we show that if (w_n)_n_³₀ is a non-degenerate Lucas sequence with real roots, then there are only finitely many non-abelian finite simple groups whose order is a member of _n_³₀. For the particular case of the classical Fibonacci and Lucas sequences, there is no such non-abelian finite simple group.

Keywords and phrases: Lucas sequences, finite simple groups.

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