Copyright © 2009 Erdal Karaduman and Ömür Deveci. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A k-nacci sequence in a finite group is a sequence of group elements x0,x1,x2,…,xn,… for which, given an initial (seed) set x0,x1,x2,…,xj−1 , each element is defined by xn=x0x1…xn−1, for   j≤n<k,  and  xn=xn−kxn−k+1…xn−1, for   n≥k. We also require that the initial elements of the sequence, x0,x1,x2,…,xj−1, generate the group, thus forcing the k-nacci sequence to reflect the structure of the group. The K-nacci sequence of a group generated by x0,x1,x2,…,xj−1 is denoted by Fk(G;x0,x1,…,xj−1) and its period is denoted by Pk(G;x0,x1,…,xj−1) . In this paper, we obtain the period of K-nacci sequences in finite polyhedral groups and the extended triangle groups.