  Geometrical structure of homogeneous isotropic models in the frame of the
metric-affine gauge theory of gravity (MAGT) is analyzed. By using general form
of gravitational Lagrangian including both a scalar curvature and various
invariants quadratic in the curvature, torsion and nonmetricity tensors,
gravitational equations of MAGT for homogeneous isotropic models are deduced.
It is shown, that obtained gravitational equations lead to generalized
cosmological Friedmann equation for the metrics by certain restrictions on
indefinite parameters of gravitational Lagrangian. Isotropic models in the
Weyl-cartan space-time are discussed.
