K-NACCI SEQUENCES IN MILLER’S GENERALIZATION OF POLYHEDRAL GROUPS

Document Type: Regular Paper

Authors

1 Department of Mathematics, Faculty of Science and Letters, Kafkas University, Turkey

2 Ataturk University, Department of Mathematics, Faculty of Science, Erzurum, Turkey

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 0 1 2 1 , , , ,j x x x x  , each element is defined by
0 1 1
1 1
for ,
for .
n
n
n k n k n
xx x j n k
x
x x x n k

   
  
   


In this paper, we examine the periods of the k-nacci sequences in Miller’s generalization of the polyhedral
groups 2,2 2;q , n,2 2;q , 2, n 2;q , 2,2 n;q , for any n  2 .

Keywords