Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0741.20025
Campbell, C.M.; Doostie, H.; Robertson, E.F.
Fibonacci length of generating pairs in groups. (English)
[A] Applications of Fibonacci numbers. Vol. 3, Proc. 3rd Int. Conf., Pisa/Italy 1988, 27-35 (1990).

[For the entire collection see Zbl 0699.00017.]\par For a 2-generator group $G$ (generated by $x$ and $y$), the authors define the Fibonacci orbit $F\sb{x,y}=\{a\sb i\}$ of $(x,y)$ by $a\sb 1=x$, $a\sb 2=y$, $a\sb{i+2}=a\sb i\cdot a\sb{i+1}$, $i\ge 1$ and the basic Fibonacci orbit $\bar F\sb{x,y}$ of basic length $m$ by the sequence $\{a\sb i\}$ of elements of $G$ such that $a\sb 1=x$, $a\sb 2=y$, $a\sb{i+2}=a\sb i\cdot a\sb{i+1}$, $i\ge 1$, where $m\ge 1$ is the least integer with $a\sb 1=a\sb{m+1}\theta$, $a\sb 2=a\sb{m+2}\theta$, for some $\theta\in\hbox{Aut}(G)$. Also, the Fibonacci length of a generator pair $(x,y)$ (LEN) is defined by the number of elements of $F\sb{x,y}$ and the length of the basic Fibonacci orbit (BLEN) by the number of elements of $\bar F\sb{x,y}$. The main aim of this paper is to compute LEN and BLEN for many classical finite groups: $D\sb{2n}$, $Q\sb 8$ and $PSL(2,p)$ ($p$ prime number).
[D.Busneag (Craiova)]

MSC 2000:: *20F05 Presentations of groups

Keywords: 2-generator group; Fibonacci orbit; Fibonacci length; number of elements

Citations: Zbl 0699.00017

Cited in: Zbl 1073.20025

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]