The Periods of \(K\)-Nacci Sequences in Centro- Polyhedral Groups and Related Groups

Omur Deveci1, Erdal Karaduman2, Colin M.Campbell3
1Department of Mathematics, Faculty of Science and Letters, Kafkas University, 36100 Kars, TURKEY
2Department of Mathematics, Faculty of Science, Atatiirk University , 25240 Erzurum, TURKEY
3School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 98S, Scotland

Abstract

The centro-polyhedral group \(\langle l,m,n\rangle\), for \(l, m, n \in \mathbb{Z}\), is defined by the presentation
\[\langle x, y, z : x^l = y^m = z^n = xyz \rangle.\]
In this paper, we obtain the periods of \(k\)-nacci sequences in centro-polyhedral groups and related groups.