THE ADJACENCY-JACOBSTHAL SEQUENCE IN FINITE GROUPS

KARADUMAN E., Akuzum Y., DEVECİ Ö.

JORDAN JOURNAL OF MATHEMATICS AND STATISTICS, cilt.12, sa.1, ss.51-58, 2019 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 1
  • Basım Tarihi: 2019
  • Dergi Adı: JORDAN JOURNAL OF MATHEMATICS AND STATISTICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.51-58
  • Atatürk Üniversitesi Adresli: Evet

Özet

The adjacency-Jacobsthal sequence and the adjacency-Jacobsthal matrix were defined by Deveci and Artun (see [5]). In this work, we consider the cyclic groups which are generated by the multiplicative orders of the adjacency-Jacobsthal matrix when read modulo alpha (alpha > 1). Also, we study the adjacency-Jacobsthal sequence modulo alpha and then we obtain the relationship among the periods of the adjacency-Jacobsthal sequence modulo alpha and the orders of the cyclic groups obtained. Furthermore, we redefine the adjacency-Jacobsthal sequence by means of the elements of 2-generator groups which is called the adjacency-Jacobsthal orbit. Then we examine the adjacency-Jacobsthal orbit of the finite groups in detail. Finally, we obtain the periods of the adjacency-Jacobsthal orbit of the dihedral group D-10 as applications of the results obtained.