The Padovan- Padovan p-Sequences in Groups

Abstract

Erdag and Deveci [13] defined the Padovan-Padovan p-sequence and they studied properties of this sequence. Then, Akuzum and Deveci [1] studied the Padovan-Padovan p-sequence modulo m. Also, they discussed the connections between the order the cyclic groups obtained and the periods of the Padovan-Padovan p-sequence according to modulo m. In this paper, we redefine the Padovan-Padovan p-sequence by means of the elements of the groups and then, we examine this sequence in the finite groups in detail. Also, we obtain the lengths of the periods of the Padovan-Padovan 4-sequence in the semidihedral group SD2m as applications of the results obtained.

Keywords

• The Padovan-Padovan p-sequence
• Group
• Period

Kaynakça

1. Reference1 Akuzum Y, Deveci O. The Padovan-Padovan p-Sequences Modulo m. 1st International Hazar Scientific Research Conference. 18-20 September, Baku, Azerbijan.
2. Reference2 Akuzum Y, Deveci O. On The Jacobsthal-Padovan p-Sequences in Groups. Topological Algebra. App. 5 (1), 2017, 63-66.
3. Reference3 Aydin H, Dikici R. General Fibonacci sequences in finite groups. Fibonacci Quart. 36(3), 1998, 216-221.
4. Reference4 Campbel CM, Campbell PP. The Fibonacci lengths of Binary polyhedral groups and related groups. Congressus Numerantium. 194, 2009, 95-102.
5. Reference5 Campbel CM, Doostie H, Robertson EF. Fibonacci Length of Generating Pairs in Groups, in Applications of Fibonacci Numbers. Vol. 3 Eds. G. E. Bergum et al. Kluwer Academic Publishers, 1990, 27-35.
6. Reference6 Deveci O. The Pell-Padovan sequences and the Jacobsthal-Padovan sequences in finite groups. Util. Math. 98, 2015, 257-27.
7. Reference7 Deveci O, Akdeniz M, Akuzum Y. The periods of the Pell-p orbits of polyhedral and Centro-polyhedral groups. Jordan Journal Math. and Stat. 10(1), 2017, 1-9.
8. Reference8 Deveci O, Akuzum Y, Karaduman E. The Pell-Padovan p-sequences and its applications. Util. Math. 98, 2015, 327-34.

9. Reference9 Deveci O. Karaduman E. On the basic k-nacci sequences in finite groups. Discrete Dyn. Nat. Soc. 2011.
10. Reference10 Deveci O, Karaduman E. The Pell sequences in finite groups. Util. Math. 96, 2015, 263-276.
11. Reference11 Deveci O, Karaduman E. On the Padovan p-numbers. Hacettepe J. Math. Stat. 46(4), 2017, 579-592.
12. Reference12 Doostie H, Hashemi M. Fibonacci lengths involving the Wall number k(n). J. Appl. Math. Comput. 20, 2006, 171-180.
13. Reference13 Erdag O, Deveci O. On The Connections Between Padovan Numbers and Padovan p-Numbers, Int. J. Open Problems Comp. Sci. Math. in Press.
14. Reference14 Knox SW. Fibonacci sequences in finite groups. Fibonacci Quart.,30(2), 1992, 116-120.
15. Reference15 Wall DD. Fibonacci series modulo m. Amer. Math. Monthly, 67, 1960, 525-532.
16. Reference16 Wilcox H.J. Fibonacci sequences of period n in groups. Fibonacci Quart. 24, 1986, 356-361.