The Jacobsthal Sequences in The Groups Q2n, Q2nXqZ2m and Q2nXZ2m

Yıl 2013, Cilt: 1 Sayı: 2, 13 - 17, 01.08.2013

Omur Deveci Gencay Saglam

Öz

In [8], Deveci et.al defined the generalized order-k Jacobsthal orbit kG of a finitely generated group GA J A, where ka ,ka A1,,a a2,, to be the sequence   of the elements of G such that ix

Anahtar Kelimeler

Group , Sequence , Length

The Jacobsthal Sequences in The Groups 2n 2n

Öz

Kaynakça

• C. M. Campbell, H. Doostie and E. F. Robertson, 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.
• O. Deveci, The Pell-Padovan sequences and the Jacobsthal-Padovan sequences in finite groups, Utilitas Mathematica, in press. O. Deveci, The polytopic-k-step Fibonacci sequences in finite groups, Discrete Dynamics in Nature and Society, 431840-1-431840-12 (2011).
• O. Deveci, The k-nacci sequences and the generalized order-k Pell sequences in the semi-direct product of finite cyclic groups, Chiang Mai Journal of Science, 40(1) (2013), 89-98.
• O. Deveci and E. Karaduman, The generalized order-k Lucas sequences in Finite groups, Journal of Applied Mathematics, 464580-1- 464580-15 (2012).
• O. Deveci and E. Karaduman, Recurrence sequences in groups, LAMBERT Acedemic Publishing, Germany, 2013.
• O. Deveci and E. Karaduman, The Pell sequences in finite groups, Utilitas Mathematica, in press. O. Deveci, E. Karaduman and G. Saglam, The Jacobsthal sequences in finite groups, Bulletin of Iranian Mathematical Society, is submitted in 2012-06-24.
• H. Doostie and P. P. Campbell, On the commutator lengths of certain classes of finitely presented groups, International Journal of Mathematics and Mathematical Sciences, Volume 2006, Article ID 74981, Pages 1-9, DOI 10.1155/IJMMS/2006/74981.
• D.L. Johnson, Presentations of Groups, 2nd edition, London Math. Soc. Student Texts 15, Cambridge University Press, Cambridge 1997.
• D. Kalman, Generalized Fibonacci numbers by matrix methods, The Fibonacci Quarterly, 20(1) (1982), 73-76.
• S.W. Knox, Fibonacci sequences in finite groups, The Fibonacci Quarterly, 30(2) (1992), 116-120.
• F. Koken and D. Bozkurt, On the Jacobsthal numbers by matrix methods, International Journal of Contemporary Mathematical Sciences, 3(13) (2008), 605-614.
• K. Lü and J. Wang, k-step Fibonacci sequence modulo m, Utilitas Mathematica, 71 (2007), 169-178.
• F. Yilmaz and D. Bozkurt, The generalized order-k Jacobsthal numbers, International Journal of Contemporary Mathematical Sciences, 4(34) (2009), 1685-1694.
• D.D. Wall, Fibonacci series modulo m, The American Mathematical Monthly, 67 (1960), 525-532.