1Mathematics Department, Science and Research Branch, Islamic Azad University, Tehran, Iran. Iran, Islamic Republic of Professor of Mathematics,
2Lecturer, 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 1992. 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 3 and exponent p has been done in 2004 by R. Dikici as well. In this paper we study all of the p-groups of nilpotency class 3 and exponent p2. This completes the study of Fibonacci length of all $p$-groups of order p4, proving that the Fibonacci length is k(p2).