## Journal of Applied Mathematics

### The Generalized Order-$k$ Lucas Sequences in Finite Groups

#### Abstract

We study the generalized order-$k$ Lucas sequences modulo $m$. Also, we define the $i$th generalized order-$k$ Lucas orbit ${l}_{A}^{i,\{{\alpha }_{1},{\alpha }_{2},\dots ,{\alpha }_{k-1}\}}$($G$) with respect to the generating set $A$ and the constants ${\alpha }_{1},{\alpha }_{2}$, and ${\alpha }_{k-1}$ for a finite group $G={\langle}A{\rangle}$. Then, we obtain the lengths of the periods of the $i$th generalized order-$k$ Lucas orbits of the binary polyhedral groups ${\langle}n,2,2{\rangle},$ ${\langle}2,n,2{\rangle},$ ${\langle}2,2,n{\rangle}$ and the polyhedral groups $(n,2,2),(2,n,2),(2,2,n)$ for $1\le i\le k$.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 464580, 15 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495053

Digital Object Identifier
doi:10.1155/2012/464580

Mathematical Reviews number (MathSciNet)
MR2889105

Zentralblatt MATH identifier
1241.11013

#### Citation

Deveci, Ömür; Karaduman, Erdal. The Generalized Order- $k$ Lucas Sequences in Finite Groups. J. Appl. Math. 2012 (2012), Article ID 464580, 15 pages. doi:10.1155/2012/464580. https://projecteuclid.org/euclid.jam/1355495053