Abstract
The idea of forming a sequence of group elements based on a Fibonacci-like recurrence relation was initially introduced by Wall in [14] and later developed by other authors, see [1], [7], [16].
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References
Aydin, H. and Smith, G.C. “Finite p-quotients of Some Cyclically Presented Groups.” J. London Math. Soc., Vol. 49 (1994): pp. 83–92.
Ayik, H., Campbell, C.M., O’Connor, J.J. and Ruskuc, N. “The Semigroup Efficiency of Direct Powers of Groups.” Proc. Internat. Conf. on Semigroups. Edited by P. Smith, E. Giraldes and P. Martins. World Scientific, Singapore, 2000, 19–25.
Campbell, C.M., Doostie, H. and Robertson, E.F. “Fibonacci Lengh of Generating Pairs in Groups.” Applications of Fibonacci Numbers. Volume 3. Edited by G.A. Bergum, et. al., Kluwer Academic Press, Dordrecht, 1990, 27–35.
Campbell, C.M., Robertson, E.F. and Williams, P.D. “On the Efficiency of Some Direct Powers of Groups.” Groups — Canberra 1989. Edited by L.G. Kovács, Lecture Notes in Math. Volume 1456 Springer, Berlin, 1990, 106–113.
Doostie, H. “Fibonacci-Type Sequences and Classes of Groups.” (Ph.D. Thesis). University of St. Andrews, Scotland, (1988).
Doostie, H. and Campbell, C.M. “Fibonacci Length of Automorphism Groups Involving Tribonacci Numbers.” Vietnam J. Math., Vol. 28 (2000): pp. 57–65.
Doostie, H. and Golamie, R. “Computing on the Fibonacci Lengths of Finite Groups.” Int. J. Appl. Math., Vol. 4 (2000): pp. 149–156.
GAP, GAP-Groups, Algorithms, and Programming, Version 4.3, Aachen, St. Andrews, 2002. (http://www-gap.dcs.st-andrews.ac.uk/-gap)
Johnson, D.L. Presentations of Groups. 2nd edition. London Math. Soc. Student Texts. Volume 15, Cambridge University Press, Cambridge 1997.
Lennox, J.C. and Wiegold, J. “Generators and Killers for Direct and Free Products.” Arch. Math. (Basel), Vol. 34 (1980): pp. 296–300.
Sims, C.C. Computation with Finitely Presented Groups. Encyclopedia of Mathematics and its Applications, Volume 48. Cambridge University Press, Cambridge 1994.
Stewart, A.G.R. and Wiegold, J. “Growth Sequences of Finitely Generated Groups II.” Bull. Austral. Math. Soc, Vol. 40 (1989): pp. 323–329.
Thomas, R.M.“The Fibonacci Groups Revisited.” Groups — St. Andrews 1989. Edited by C.M. Campbell and E.F. Robertson. Cambridge University Press, Cambridge, 1991, 445–454.
Wall, D.D. “Fibonacci Series modulom.” Amer. Math. Monthly, Vol. 67 (1960): pp. 525–532.
Wiegold, J. “The Schur Multiplier: an Elementary Approach.” Groups — St. Andrews 1981. Edited by C.M. Campbell and E.F. Robertson, Cambridge University Press, Cambridge, 1982, 137–154.
Wilcox, H.J. “Fibonacci Sequences of Period n in Groups.” The Fibonacci Quarterly, Vol. 24 (1986) : pp. 356–361.
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Campbell, C.M., Campbell, P.P., Doostie, H., Robertson, E.F. (2004). On the Fibonacci Length of Powers of Dihedral Groups. In: Howard, F.T. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-0-306-48517-6_9
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