Advanced Search

Query:

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

Format:

Display: entries per page entries

Zbl 0758.20006
Knox, Steven W.
Fibonacci sequences in finite groups. (English)
[J] Fibonacci Q. 30, No.2, 116-120 (1992). ISSN 0015-0517

A $k$-nacci sequence in a finite group $G$ is a sequence of group elements $x\sb 0,x\sb 1,\dots,x\sb n,\dots$ for which, given an initial generating set $x\sb 0,\dots,x\sb{j-1}$ for $G$, each element is defined by $$x\sb n=\cases x\sb 0x\sb 1\cdots x\sb{n-1}&\text{for $j\le n<k$}\\x\sb{n-k}x\sb{n-k+1}\cdots x\sb{n-1}&\text{for $n\ge k$}.\endcases$$ A $k$-nacci sequence certainly reflects the structure of $G$. A finite group $G$ is called $k$-nacci sequenceable if there exists a $k$-nacci sequence of $G$ such that every element of $G$ appears in the sequence. It is shown that a $k$-nacci sequence in a finite group $G$ is simply periodic. This leads to a complete description of the 2-nacci sequenceable groups. A 2-nacci sequenceable group is cyclic.
[G.Rosenberger (Dortmund)]

MSC 2000:: *20D60 Arithmetic and combinatorial problems on finite groups
11B39 Special numbers, etc.
20F05 Presentations of groups

Keywords: generating set; $k$-nacci sequence; $k$-nacci sequenceable; finite group; 2-nacci sequenceable groups

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

	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]