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Zbl 0986.20034
Doostie, H.; Campbell, C.M.
Fibonacci length of automorphism groups involving Tribonacci numbers.
(English)
[J] Vietnam J. Math. 28, No.1, 57-65 (2000). ISSN 2305-221X; ISSN 2305-2228/e

For a finite group $G=\langle a,b\rangle$ with two generators the Fibonacci length is the least integer $n$ such that for the sequence $x_1=a$, $x_2=b$, $x_{i+2}=x_ix_{i+1}$ ($i\ge 1$) of elements of $G$, $x_{n+1}=x_1$ and $x_{n+2}=x_2$. In the paper under review the above notion is generalized for a finite group with 3 generators and then the authors calculate the Fibonacci length of the groups $\Aut(D_{2n})$ and $\Aut(Q_{2^n})$.
MSC 2000:
*20F05 Presentations of groups
20D60 Arithmetic and combinatorial problems on finite groups
11B39 Special numbers, etc.
20D45 Automorphisms of finite groups

Keywords: automorphism groups; finite groups; generators; Fibonacci lengths

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