Fibonacci lengths for certain metacyclic groups

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Let G = <A> be a finitely generated group, where A = {a(1), a(2), - - - a(n)} The sequence x(i) = alpha(i+1) for 0 less than or equal to i less than or equal to n - 1 and x(i+n), = Pi(j=1)(n) x(i+j-1) for i greater than or equal to 0 is called the Fibonacci orbit of G with respect to the generating set A, denoted by FA(G). If F-A(G) is periodic, we call the length of the period of the sequence the Fibonacci length of G with respect to A, written LENA(G). In this paper, we examine the Fibonacci length of certain groups including some due to Fox and certain Fibonacci groups.

Original languageEnglish
Pages (from-to)215-222
Number of pages8
JournalAlgebra Colloquium
Issue number2
Publication statusPublished - Jun 2004


  • group
  • Fibonacci sequence
  • Fibonacci length


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