The cyclic sequences in non-Abelian groups

Abstract

In this paper, we describe the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the non-abelian groups and then we investigate them in non-abelian finite groups in detail. Furthermore, we give the lengths of the periods of the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the polyhedral group $(n,2,2)$ with respect to the generating triple $(a,b,c)$ as applications of the results produced.

Keywords:

• Group
• period
• the cyclic sequence

2000 Mathematics Subject Classification:

• 11K31
• 11B50
• 20F05
• 43A30

Acknowledgments

The authors thank the referee for their valuable suggestions, which improved the presentation of the paper.