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Fibonacci lengths involving the Wall number $k(n)$. (English) Zbl 1083.20031
Summary: Two infinite classes of special finite groups are considered. (The group $G$ is special, if $G'$ and $Z(G)$ coincide.) Using certain sequences of numbers we give explicit formulas for the Fibonacci lengths of these classes which involve the well-known Wall numbers $k(n)$.

20F05Generators, relations, and presentations of groups
11B39Fibonacci and Lucas numbers, etc.
20D60Arithmetic and combinatorial problems on finite groups
Full Text: DOI
[1] Ali Reza Ashrafi,Counting the centralizers of some finite groups, J. Appl. Math. & Computing,7 (2000), 115--124. · Zbl 0951.20013
[2] H. Aydin and G. C. Smith,Finite p-quotients of some cyclically presented groups, J. London Math. Soc.49 (1994), 83--92. · Zbl 0807.20029
[3] M. J. Beetham and C. M. Campbell,A note on the Todd-Coxeter coset enumeration algorithm, Proc. Edinburgh Math. Soc.20 (1976), 73--79. · Zbl 0328.20032 · doi:10.1017/S0013091500015790
[4] C. M. Campbell, H. Doostie and E. F. Robertson,Fibonacci length of generating pairs in groups, in: Applications of Fibonacci numbers, G. A. Bergumet (eds.), Vol. 5, 1990, 27-35. · Zbl 0741.20025
[5] C. M. Campbell, P. P. Campbel, H. Doostie and E. F. Robertson,Fibonacci length for certain metacyclic group, Algebra Colloquium11 (2) (2004), 215--222. · Zbl 1069.20021
[6] H. Doostie,Fibonacci-type sequences and classes of groups, Ph. D. Thesis, The University of St. Andrews, Scotland, 1988.
[7] H. Doostie and R. Golamie,Computing on the Fibonacci lengths of finite groups, Internat. J. Appl. Math.4 (2000), 149--156. · Zbl 1172.20304
[8] Ali-Reza Jamali,Deficiency zero non-metacyclic p-groups of order less than 1000, J. Appl. Math. & Computing,16 (2004), 303--306. · Zbl 1055.20014 · doi:10.1007/BF02936170
[9] D. D. Wall,Fibonacci series modulo m, Amer. Math. Monthly67 (1960), 525--532. · Zbl 0101.03201 · doi:10.2307/2309169