Journal of Applied Mathematics

The Generalized Order- k Lucas Sequences in Finite Groups

Ömür Deveci and Erdal Karaduman

Full-text: Open access

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 , { α 1 , α 2 , , α k - 1 } ( G ) with respect to the generating set A and the constants α 1 , α 2 , and α k - 1 for a finite group G = A . Then, we obtain the lengths of the periods of the i th generalized order- k Lucas orbits of the binary polyhedral groups n , 2 , 2 〉, 2 , n , 2 〉, 2 , 2 , n and the polyhedral groups ( n , 2 , 2 ) , ( 2 , n , 2 ) , ( 2 , 2 , n ) for 1 i k .

Article information

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

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
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


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