Fibonacci Lengths of Certain Nilpotent 2–Groups

Abstract

In this paper, we study two classes of 2–generated 2–groups of nilpotency class 2 classified by Kluempen in 2002 and also a class of finite 2–groups of high nilpotency class for their Fibonacci lengths. Their involvement in certain interesting sequences of Tribonacci numbers gives us some explicit formulas for the Fibonacci lengths and this adds to the small class of finite groups for which the Fibonacci length are known.