  We examine the scalings of X-ray luminosity, temperature, and dark matter or
galaxy velocity dispersion for galaxy groups in an LCDM cosmological
simulation, which incorporates gravity, gas dynamics, radiative cooling, and
star formation, but no substantial non-gravitational heating. In agreement with
observations, the simulated L_X-sigma and L_X-T_X relations are steeper than
those predicted by adiabatic simulations or self-similar models, with
L_X\propto sigma^{4.4} and L_X\propto T_X^{2.6} for massive groups and
significantly steeper relations below a break at sigma~180 km/s (T_X~0.7 keV),
but T_X-sigma is fairly close to self-similar, with T_X\propto sigma^{1.75}.
The entropy of hot gas in low mass groups is higher than predicted by
self-similar scaling, and agrees with observations that suggest an "entropy
floor". The steeper scalings of the luminosity relations are driven by
radiative cooling, which reduces the hot gas fraction from 50% of the total
baryons at sigma \approx 500 km/s to 20% at sigma \approx 100 km/s. A secondary
effect is that hot gas in smaller systems is less clumpy, further driving down
L_X. A smaller volume simulation with eight times higher mass resolution
predicts nearly identical X-ray luminosities at a given group mass,
demonstrating the insensitivity of the predicted scaling relations to numerical
resolution. There remain some quantitative discrepancies: the predicted mass
scale of the L_X-T_X and L_X-sigma breaks is somewhat too low, and the
luminosity-weighted temperatures are too high at a given sigma. We conclude
that radiative cooling has an important quantitative impact on group X-ray
properties and can account for many of the observed trends that have been
interpreted as evidence for non-gravitational heating. (abridged)
