| Abstrakt: |
In this paper, we extend the balancing sequences to groups. In the first part of paper, we study the balancing sequences in 2-generator groups and then give some useful results concerning the periods of the balancing sequences in finite groups. Also, we calculate the periods of balancing sequences in the polyhedral groups (2,2,2), (n, n, 2), (2, n, 2) and (2, 2, n) with respect to the generating pair (x, y). In the later part of the paper, to improve balancing sequences, we define the fc-step balancing sequences and examine the periods of these sequences when read modulo m. Furthermore, we redefine the &-step balancing sequences by means of group elements and then examine them in finite groups. Finally, we compute the periods of the 3-step balancing sequences in the polyhedral groups (2, 2,2), (2,2, n), (2, n, 2) and (2,2, n) with respect to the generating triple (re, y, z) applications of the results obtained. [ABSTRACT FROM AUTHOR] |
