  We study the electron-electron interaction contribution to the conductivity
of two-dimensional In$_{0.2}$Ga$_{0.8}$As electron systems in the diffusion
regime over the wide conductivity range, $\sigma\simeq(1-150) G_0$, where
$G_0=e^2/(2\pi^2\hbar)$. We show that the data are well described within the
framework of the one-loop approximation of the renormalization group (RG)
theory when the conductivity is relatively high, $\sigma \gtrsim 15 G_0$. At
lower conductivity, the experimental results are found to be in drastic
disagreement with the predictions of this theory. The theory predicts much
stronger renormalization of the Landau's Fermi liquid amplitude, which controls
the interaction in the triplet channel, than that observed experimentally. A
further contradiction is that the experimental value of the interaction
contribution does not practically depend on the magnetic field, whereas the RG
theory forecasts its strong decrease due to decreasing diagonal component of
the conductivity tensor in the growing magnetic field.
