The adjacency-Jacobsthal-Hurwitz sequences in groups

ABSTRACT

In [3], 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.

KEYWORDS:

• Group
• period
• the Adjacency-Jacobsthal-Hurwitz Sequence

2000 MATHEMATICS SUBJECT CLASSIFICATION:

• 11B50
• 20F05
• 11C20
• 20D60