The adjacency-Jacobsthal-Hurwitz sequences in groups |
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Authors: | Ömür Deveci Erdal Karaduman |
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Institution: | 1. Department of Mathematics, Faculty of Science and Letters, Kafkas University, Kars, Turkey;2. Department of Mathematics, Faculty of Science, Atatürk University, Erzurum, Turkey |
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Abstract: | In 3 Deveci, O., Aküzüm, Y. (in press). The adjacency-Jacobsthal-Hurwitz type numbers. Filomat. Google Scholar]], Deveci and Aküzüm defined the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind. In this work, firstly we produce the cyclic groups from the multiplicative orders of the generating matrices of the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind when read modulo λ and we study the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind modulo λ. Then, we give the relationship between the orders of the cyclic groups obtained and the periods of the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind modulo λ. Further, we extend the adjacency-Jacobsthal-Hurwitz sequences of the first and second kind to groups and then we examine these sequences in the quaternion group Q8 in detail. |
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Keywords: | Group period the Adjacency-Jacobsthal-Hurwitz Sequence |
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