B. Ahmadi - Mathematics Department, Science and Research Branch, Islamic Azad University, Tehran, Iran. Iran, Islamic Republic of Professor of Mathematics,
H. Doostie - Lecturer, Lahijan Islamic Azad University, Lahijan, Iran Iran, Islamic Republic of Lecturere, Ph.D. Student (at present).

The Fibonacci lengths of the finite p-groups have been studied by R. Dikici and co-authors since ۱۹۹۲. All of the considered groups are of exponent p, and the lengths depend on the celebrated Wall number k(p). The study of p-groups of nilpotency class ۳ and exponent p has been done in ۲۰۰۴ by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class ۳ and exponent p۲. This completes the study of Fibonacci length of all p-groups of order p۴, proving that the Fibonacci length is k(p۲).

Fibonacci length, p-groups, Nilpotency class۳