Fibonacci lengths of all finite p-groups of exponent p2

Abstract

The Fibonacci lengths of finite p-groups were studied by Dikici and coauthors since 1992. All considered groups are of exponent p and the lengths depend on the Wall number k(p). The p-groups of nilpotency class 3 and exponent p were studied in 2004 also by Dikici. In the paper, we study all p-groups of nilpotency class 3 and exponent p 2. Thus, we complete the study of Fibonacci lengths of all p-groups of order p 4 by proving that the Fibonacci length is k(p 2).