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Fibonacci length of automorphism groups involving Tribonacci numbers. (English) Zbl 0986.20034
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:
 20F05 Generators, relations, and presentations of groups 20D60 Arithmetic and combinatorial problems on finite groups 11B39 Fibonacci and Lucas numbers, etc. 20D45 Automorphisms of finite groups