COMPUTATIONAL RESULTS ON FINITE P-GROUPS OF EXPONENT P2

Subject Areas : International Journal of Mathematical Modelling & Computations

B. Ahmadi ¹ , H. Doostie ²

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

Received: 2016-04-14 Accepted : 2016-04-14 Published : 2016-03-20

Keywords: Fibonacci length, $p$-groups, Nilpotency class3,

Abstract :

The Fibonacci lengths of the finitep-groups have been studied by R. Dikici and co-authors since 1992. All of the considered groups are of exponentp, and the lengths depend on the celebrated Wall numberk(p). The study ofp-groups of nilpotency class 3 and exponentphas been done in 2004 by R. Dikici as well. In this paper we study all of thep-groups of nilpotency class 3 and exponentp2. This completes the study of Fibonacci length of all $p$-groups of orderp4, proving that the Fibonacci length isk(p2).