Skip to main content
SpringerLink
Log in

Wall and Vinson Revisited

  • Chapter
Applications of Fibonacci Numbers

Abstract

Let G be a finite group. We define a family of recurrences, parameterized by natural numbers n, via equations

$${{x}_{i}} = {{x}_{{i - 1}}}{{x}_{{i - 2}}} \cdots {{x}_{{i - n}}}.$$
(Rn)

The work of the first two authors was supported by Ataturk University, Erzurum, Turkey

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aydin, H. “Recurrence Relations in Finite Nilpotent Groups.” Ph.D. thesis, Bath (1991).

    Google Scholar 

  2. Aydin, H. and Smith, G.C. “Remarks on Fibonacci Sequences in Groups 1.” Bath Mathematics and Computer Science Technical Report 91–50, University of Bath 1991.

    Google Scholar 

  3. Aydin, H. and Smith, G.C. “Finite p-Quotients of Some Cyclically Presented Groups.” J. Lond Math. Soc. to appear.

    Google Scholar 

  4. Campbell, C.M., Doostie, H. and Robertson, E.F. “Fibonacci Length of Generating Pairs in Groups.” Applications of Fibonacci Numbers, Volume 3. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam, Dorchecht, The Netherlands, (1990): pp. 27–35.

    Chapter  Google Scholar 

  5. Cannon, J.J. An introduction to the group theory language Cavley, in Computational Group Theory. Edited by M.D. Atkinson, Academic Press, London, (1984): pp. 145–183.

    Google Scholar 

  6. Doostie, H. “Fibonacci-type Sequences and Classes of Groups.” Ph.D. thesis, St Andrews (1988).

    Google Scholar 

  7. Dresel, L.A.G. “Letter to the Editor.” The Fibonacci Quarterly, Vol. 15 (1977): p. 346.

    Google Scholar 

  8. Heed, J.J. “Wieferichs and the Problem z(p 2) = z(p)” The Fibonacci Quarterly, Vol. 22 (1964): pp. 116–118.

    MathSciNet  Google Scholar 

  9. Lucas, E. “Théorie des fonctions numériques simplement périodiques.” Amer. J. Math., Vol. 1 (1878): pp. 184–240

    Article  MathSciNet  Google Scholar 

  10. Lucas, E. “Théorie des fonctions numériques simplement périodiques.” Amer. J. Math., Vol. 1 (1878): 289-321.

    Article  MathSciNet  Google Scholar 

  11. Pinch, R.G.E. “Linear Recurrent Sequences modulo prime powers.” To appear, Proc. 3rd IMA Conference on Coding and Cryptography, Cirencester, England. December 1991.

    Google Scholar 

  12. Ribenboim, P. The Little Book of Big Primes, Springer-Verlag (1991).

    MATH  Google Scholar 

  13. Reeds, J.A. and Sloane, N.J.A. “Shift Register synthesis (modulo m).” SIAM J. Comput., Vol. 14 (1985): pp. 505–513.

    Article  MathSciNet  MATH  Google Scholar 

  14. Somer, L. “The Divisibility Properties of Primary Lucas Recurrences with Respect to Primes.” The Fibonacci Quarterly, Vol. 18.4 (1980): pp. 316–334.

    MathSciNet  Google Scholar 

  15. Sutor, R.S. (ed.) AXIOM user guide, NAG Ltd, (1991).

    Google Scholar 

  16. Thomas, R.M. “The Fibonacci Groups Revisited.” Proceedings of Groups St. Andrews 1989, Volume 2 LMS Lecture Note Series 160, CUP. Edited by C.M. Campbell and E.F. Robertson, (1991): pp. 445–454.

    Google Scholar 

  17. Vinson, J. “The Relations of the Period Modulo m to the Rank of Apparition of m in the Fibonacci Sequence.” The Fibonacci Quarterly, Vol. 1 (1963): pp. 37–45.

    MathSciNet  MATH  Google Scholar 

  18. Wall, D.D. “Fibonacci Series Modulo m.” Amer. Math. Monthly, Vol. 67 (1960): pp. 525–532.

    Article  MathSciNet  MATH  Google Scholar 

  19. Wilcox, H.J. “Fibonacci Sequences of period n in Groups.” The Fibonacci Quarterly, Vol. 24 (1986): pp. 356–361.

    MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Huseyin Aydin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramazan Dikici
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Geoff C. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, South Dakota State University, Box 2201, Brookings, South Dakota, 57007-0194, USA

    Gerald E. Bergum

  2. Ministry of Education, Government House Z 50, Nicosia, Cyprus

    Andreas N. Philippou

  3. Department of Mathematics, Statistics and Computer Science, University of New England, Armidale, New South Wales, 2351, Australia

    Alwyn F. Horadam

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Aydin, H., Dikici, R., Smith, G.C. (1993). Wall and Vinson Revisited. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2058-6_6

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-2058-6_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4912-2

  • Online ISBN: 978-94-011-2058-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation