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Fibonacci lengths involving the Wall number $k(n)$. (English) Zbl 1083.20031
Summary: Two infinite classes of special finite groups are considered. (The group $G$ is special, if $G'$ and $Z(G)$ coincide.) Using certain sequences of numbers we give explicit formulas for the Fibonacci lengths of these classes which involve the well-known Wall numbers $k(n)$.

##### MSC:
 20F05 Generators, relations, and presentations of groups 11B39 Fibonacci and Lucas numbers, etc. 20D60 Arithmetic and combinatorial problems on finite groups
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##### References:
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