  The nonsoluble length $\lambda(G)$ of a finite group $G$ is defined as the
minimum number of nonsoluble factors in a normal series of $G$ each of whose
quotients either is soluble or is a direct product of nonabelian simple groups.
The generalized Fitting height of a finite group $G$ is the least number
$h=h^*(G)$ such that $F^*_h(G)=G$, where $F^*_1(G)=F^*(G)$ is the generalized
Fitting subgroup, and $F^*_{i+1}(G)$ is the inverse image of
$F^*(G/F^*_{i}(G))$. In the present paper we prove that if $\lambda (J)\leq k$
for every 2-generator subgroup $J$ of $G$, then $\lambda(G)\leq k$. It is
conjectured that if $h^*(J)\leq k$ for every 2-generator subgroup $J$, then
$h^*(G)\leq k$. We prove that if $h^*(\langle x,x^g\rangle)\leq k$ for all
$x,g\in G$ such that $\langle x,x^g\rangle$ is soluble, then $h^*(G)$ is
$k$-bounded.
