The Generalized Order- 𠑘 Lucas Sequences in Finite Groups

Ömür Deveci and Erdal Karaduman

Journal of Applied Mathematics, 2012, vol. 2012, 1-15

Abstract:

We study the generalized order- 𠑘 Lucas sequences modulo ð ‘š . Also, we define the ð ‘– th generalized order- 𠑘 Lucas orbit ð ‘™ ð ‘– , { ð ›¼ 1 , ð ›¼ 2 , … , ð ›¼ 𠑘 − 1 } ð ´ ( ð º ) with respect to the generating set ð ´ and the constants ð ›¼ 1 , ð ›¼ 2 , and ð ›¼ 𠑘 − 1 for a finite group ð º = ⟨ ð ´ âŸ© . Then, we obtain the lengths of the periods of the ð ‘– th generalized order- 𠑘 Lucas orbits of the binary polyhedral groups ⟨ ð ‘› , 2 , 2 ⟩ , ⟨ 2 , ð ‘› , 2 ⟩ , ⟨ 2 , 2 , ð ‘› ⟩ and the polyhedral groups ( ð ‘› , 2 , 2 ) , ( 2 , ð ‘› , 2 ) , ( 2 , 2 , ð ‘› ) for 1 ≤ ð ‘– ≤ 𠑘 .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:464580

DOI: 10.1155/2012/464580

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