COMPUTATIONAL RESULTS ON FINITE P-GROUPS OF EXPONENT P2

Authors

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).

Abstract

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).
 

Keywords