156
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

The cyclic sequences in non-Abelian groups

, &
Pages 2956-2962 | Received 06 Jan 2022, Accepted 18 Jan 2023, Published online: 11 Feb 2023

References

  • Aydin, H., Dikici, R. (1998). General Fibonacci sequences in finite groups. Fibonacci Q. 36(3):216–221.
  • Campbell, C. M., Campbell, P. P. (2004). On the Fibonacci length of powers of dihedral groups. In: Howard, F. T., ed., Applications of Fibonacci Numbers, Vol. 9. Dordrecht: Kluwer Academic Publisher, pp. 69–85.
  • Campbell, C. M., Doostie, H., Robertson, E. F. (1990). Fibonacci length of generating pairs in groups. In: Bergum, G. E., ed. Applications of Fibonacci Numbers, Vol. 3. Dordrecht: Kluwer Academic Publishers/Springer, pp. 27–35.
  • Conway, J. H., Coxeter, H. S. M., Shephard, G. C. (1972). The centre of a finitely generated group. Tensor. New Series 25:405–418.
  • Coxeter, H. S. M., Moser, W. O. J. (1972). Generators and Relations for Discrete Groups, 3rd ed. Berlin: Springer.
  • DeCarli, D. J. (1970). A generalized Fibonacci sequence over an arbitrary ring. Fibonacci Q. 8(2):182–184.
  • Deveci, O., Shannon, A. G. (2021). The complex-type k -Fibonacci sequences and their applications. Commun. Algebra. 49(3):1352–1367. DOI: 10.1080/00927872.2020.1834573.
  • Deveci, O., Shannon, A. G. (2018). The quaternion-Pell sequence. Commun. Algebra, 46(12):5403–5409. DOI: 10.1080/00927872.2018.1468906.
  • Deveci, O., Karaduman, E. (2015). The Pell sequences in finite groups. Util Math. 96:263–276.
  • Deveci, O., Karaduman, E., Campbell, C. M. (2011). On the k -nacci sequences in finite binary polyhedral groups. Algebra Colloq. 18(1):945–954. DOI: 10.1142/S1005386711000824.
  • Doostie, H., Hashemi, M. (2006). Fibonacci lengths involving the Wall number k(n). J. Appl. Math. Comput. 20(1):171–180.
  • Hashemi, M., Mehraban, E. (2021). The generalized order k-Pell sequences in some special groups of nilpotency class 2. Commun. Algebra 50(4):1768–1784. DOI: 10.1080/00927872.2021.1988959.
  • Karaduman, E., Ayd in, H. (2009). k-nacci sequences in some special groups of finite order. Math. Comput. Modell. 50(1–2):53–58.
  • Karaduman, E., Ayd in, H. (2003). General 2-step Fibonacci sequences in nilpotent groups of exponent p and nilpotency class 4. Appl. Math. Comp. 141(2–3):491–497.
  • Kilic, E., Tasci D. (2006). The generalized Binet formula, representation and sums of the generalized order-k Pell numbers. Taiwanese J. Math. 10(6):1661–1670.
  • Knox, S. W. (1992). Fibonacci sequences in finite groups. Fibonacci Q. 30(2):116–120.
  • Lu, K., Wang, J. (2006). k-step Fibonacci sequence modulo m. Util. Math. 71:169–177.
  • Mehraban, E., Hashemi, M. (2021). Fibonacci length and the generalized order k-Pell sequences of the 2-generator p-groups of nilpotency class 2. J. Algebra Appl. DOI: 10.1142/S0219498823500615.
  • Ozkan, E. (2014). Truncated Lucas sequences and its period. Appl. Math. Comput. 232:285–291. DOI: 10.1016/j.amc.2014.01.014.
  • Ozkan, E. (2003). 3-step Fibonacci sequences in nilpotent groups. Appl. Math. Comput. 144(2–3):517–527.
  • Shannon, A. G. (1979). Generalized Fibonacci numbers as elements of ideals. Fibonacci Q. 17(4):347–349.
  • Wall, D. D. (1960). Fibonacci series modulo m. Amer. Math. Monthly 67(6):525–532. DOI: 10.1080/00029890.1960.11989541.
  • Wilcox, H. J. (1986). Fibonacci sequences of period n in Groups. Fibonacci Q. 24(4):356–361.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.