Fibonacci length of direct products of groups. (English) Zbl 1123.20029
Summary: For a non-Abelian finite group the Fibonacci length of with respect to the ordered generating set is the least integer such that for the sequence of elements , , , , of , the equations , hold. The question posed in 2003 by P. P. Campbell is “Is there any relationship between the lengths of finite groups , and ?” In this paper we answer this question when at least one of the groups is a non-Abelian 2-generated group.
|20F05||Generators, relations, and presentations of groups|
|20D60||Arithmetic and combinatorial problems on finite groups|
|11B39||Fibonacci and Lucas numbers, etc.|
|20D40||Products of subgroups of finite groups|