  Upcoming X-ray surveys like eROSITA require precise calibration between X-ray
observables and mass down to the low mass regime to set tight constraints on
the fundamental cosmological parameters. Since an individual mass measurement
is only possible for a relatively small number of objects it is crucial to have
robust and well understood scaling relations that relate the total mass to
easily observable quantities. The main goal of this work is to constrain the
galaxy group scaling relations corrected for selection effects, and to quantify
the influence of non-gravitational physics at the low-mass regime. We analyzed
XMM-Newton observations for a complete sample of galaxy groups selected from
the ROSAT All-Sky Survey and we compared the derived scaling properties with a
galaxy cluster sample. To investigate the role played by the different
non-gravitational processes we then compared the observational data with the
predictions of hydrodynamical simulations. After applying the correction for
selection effects (e.g. Malmquist bias) the L-M relation is steeper than the
observed one. Its slope is also steeper than the value obtained by using the
more massive systems of the HIFLUGCS sample. This behaviour can be explained by
a gradual change of the true L-M relation which should be taken into account
when converting the observational parameters into masses. The other observed
scaling relations (not corrected for selection biases) do not show any break
although the comparison with the simulations suggests that feedback processes
play an important role in the formation and evolution of galaxy groups. Thanks
to our master sample of 82 objects spanning two order of magnitude in mass we
tightly constrain the dependence of the gas mass fraction on the total mass,
finding almost a factor of two difference between groups and clusters.
