Abstract. For a
nonabelian finite group G = <a_{1}, a_{2}, …,a_{n}>
the Fibonacci length of G with
respect to the ordered generating set A
= {a_{1}, a_{2}, …, a_{n}} is the least integer
l such that for the sequence of elements x_{i} = a_{i},
1 i
n,
x_{n}_{+I }= ,
I 1, of G,
the equations x_{l}_{+i }= a_{i}, 1 i
n
hold. The question posed in 2003 by P.P. Campbell that "Is there any relationship
between the lengths of finite groups G,
H and G x H?" In this
paper we answer this question when at least one of the groups is a
nonabelian 2generated group.
