zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fibonacci length of generating pairs in groups. (English) Zbl 0741.20025
Applications of Fibonacci numbers. Vol. 3, Proc. 3rd Int. Conf., Pisa/Italy 1988, 27-35 (1990).

[For the entire collection see Zbl 0699.00017.]

For a 2-generator group G (generated by x and y), the authors define the Fibonacci orbit F x,y ={a i } of (x,y) by a 1 =x, a 2 =y, a i+2 =a i ·a i+1 , i1 and the basic Fibonacci orbit F ¯ x,y of basic length m by the sequence {a i } of elements of G such that a 1 =x, a 2 =y, a i+2 =a i ·a i+1 , i1, where m1 is the least integer with a 1 =a m+1 θ, a 2 =a m+2 θ, for some θAut(G). Also, the Fibonacci length of a generator pair (x,y) (LEN) is defined by the number of elements of F x,y and the length of the basic Fibonacci orbit (BLEN) by the number of elements of F ¯ x,y . The main aim of this paper is to compute LEN and BLEN for many classical finite groups: D 2n , Q 8 and PSL(2,p) (p prime number).


MSC:
20F05Generators, relations, and presentations of groups