  Using hydrodynamical simulations of the LCDM cosmology, that include both
radiative cooling and a phenomenological model for star formation and
supernovae feedback, we investigate the impact of galaxy formation on the X-ray
properties of groups at redshift zero. Motivated by the observed ``break'' in
the L_x-T_x relation at kT~1-2keV, our feedback model is based on the
assumption that supernovae imprint a temperature scale on the hot gas, with the
star formation rate and corresponding reheated gas mass then depending only on
the available energy budget. We demonstrate that a strong feedback model with a
heating temperature comparable to this break (kT_=2keV), and an energy budget
twice that available from supernovae (epsilon=2), raises the core entropy of
groups sufficiently to produce an adequate match to their observed X-ray
properties. A lower value of epsilon increases the star formation rate without
significantly affecting the X-ray properties of groups, and a model with
epsilon~0.1 reproduces the observed fraction of baryons in stars. However, a
heating temperature which is lower than the virial temperatures of the groups
leads to an excess of cooling gas that boosts their X-ray luminosities, due to
the failure of the reheated material to escape from the gravitational
potential. A limited study of numerical resolution effects reveals that the
temperature of poorly-resolved objects is underestimated, therefore (in our
case) a fully-resolved group population would lead to a steeper L_x-T_x
relation, bringing our results into even better agreement with the
observations.
