Fibonacci length of automorphism groups involving Tribonacci numbers
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 \(x_1=a\), \(x_2=b\), \(x_{i+2}=x_ix_{i+1}\) (\(i\geq 1\)) 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 \(\Aut(Q_{2^n})\).
scientific article; zbMATH DE number 1556828