Fibonacci Length of some subgroups of Sn

Subject Areas : Statistics

Zahra Shafiei kalaleh ¹ , Mohammad Maghasedi ²

1 - Department of Mathematics, Islamic Azad University, Karaj branch, Karaj, Alborz
2 - Department of Mathematics, Islamic Azad University, Karaj branch, Karaj, Alborz

Received: 2021-03-09 Accepted : 2021-10-20 Published : 2023-01-21

Keywords: دنباله فیبوناتچی, گروه متناهی, طول فیبوناتچی,

Abstract :

Calculating and deriving the properties of the Fibonacci length of finite groups have been done since 1990, where the Fibonacci length of the finite group is defined to be the least integer such that for the Fibonacci sequence of the elements of the group , all of the equalities hold. In this paper we calculate Fibonacci length of 2- sylow subgroups of , by giving suitable generating sets for it. m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m

References:

 

‎[1] H. Aydin, R. Dikici, and C. G. Smith, (1993). "Wall and Winson revisited", In Applications of Fibonacci Numbers, 5.

‎[2] H. Aydin, and C. G. Smith, (1994). "It Finite ‎p‎‏-quotients of some cyclically presented groups", J. London Math. Soc, 49.

[3] Q. J. Brinson, (1992). "Complete Fibonacci sequences in finite fields", Fibonnaci Quarterly, 30, 295-304.

[4] C. M. Compbell, H. Doostie and E. F. Robertson, (1990). "Fibonacci length of generating pairs in groups", In Applications of Fibonacci Numbers, 3.

[5] P. P. Campbell, H. Doostie and E. F. Robertson, (2004). "On the Fibonacci length of dihedral groups", In Applications of Fibonacci Numbers, 9.

[6] P. P. Campbell, H. Doostie and E. F. Robertson, (2004). "Fibonacci length for certain metacyclic groups", Algebra Colloquium, 11:2.

[7] H. Doostie and C. M. Campbell, (2000). "Fibonacci length of automorphism groups involving Tribonacci numbers", Vietnam J. of Math., 28:1.

[8] H. Doostie and R. Golamie, (2000). "Computing on the Fibonacci length of finite groups". Internat. J. Appll. Math. 4:2.

[9] H. Doostie, M. Maghasedi. (2005) "Fibonacci length of direct products of groups,"Vietnam J. of Math., 33 (2), 189-197.

 [10] GAP, (2002). "GAP-groups, Algorithms and Programming, version 4.3, Aachen", St-Andrews.

[11] D. D. Wall, (1960). "Fibonacci series modulo ", Amer. Math. Montly, 67.

[12] H. J. Wilcox, (1986). "Fibonacci sequences of period n in groups", Fibonacci Quarterly, 24