  On the basis of the previously formulated mathematical model of a statistical
system with scalar interaction of fermions and the theory of
gravitational-scalar instability of a cosmological model based on a
one-component statistical system of scalarly charged degenerate fermions (\MIO
models), the possibility of the formation of black holes in the early Universe
using the mechanism of gravitational-scalar instability, which ensures the
exponential growth of perturbations. The evolution of spherical masses in the
\MIO model, as well as the evolution of black holes with allowance for their
evaporation, is studied. The argumentation of the possibility of the formation
of black holes in the early Universe with the help of the proposed mechanism is
given, and a numerical model is constructed that confirms this argumentation.
The range of parameters of the \MIO model, which ensures the growth of black
hole masses in the early Universe up to $10^4\div10^6 M_\odot$, is identified.
