The Jacobsthal Sequences in Finite Groups

Document Type : Research Paper


1 Department of Mathematics‎, ‎Faculty of Science‎ ‎and Letters‎, ‎Kafkas University‎, ‎36100 Kars‎, ‎Turkey.

2 Department of Mathematics‎, ‎Faculty of Science‎, ‎Atat‎urk University‎, ‎25240 Erzurum‎, ‎Turkey.


Abstract In this paper, we study the generalized order- Jacobsthal sequences modulo for and the generalized order-k Jacobsthal-Padovan sequence modulo for . Also, we define the generalized order-k Jacobsthal orbit of a k-generator group for and the generalized order-k Jacobsthal-Padovan orbit a k-generator group for . Furthermore, we obtain the lengths of the periods of the generalized order-3 Jacobsthal orbit and the generalized order-3 Jacobsthal-Padovan orbit of the direct product, and the semidirect product .


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