We examine the scalings of X-ray luminosity , temperature , and dark matter or galaxy velocity dispersion for galaxy groups in a \Lambda CDM 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 \approx 180 km/s ( T _ { X } \approx 0.7 keV ) . The T _ { X } - \sigma relation is fairly close to the self-similar scaling relation , with T _ { X } \propto \sigma ^ { 1.75 } , provided that the velocity dispersion is estimated from the dark matter or from \gtrsim 10 galaxies . The entropy of hot gas in low mass groups is higher than predicted by self-similar scaling or adiabatic simulations , and it agrees with observational data that suggest an “ entropy floor. ” The steeper scalings of the luminosity relations are driven by radiative cooling , which reduces the hot ( X-ray emitting ) 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 . The higher resolution simulation predicts higher hot gas fractions at a given group mass , and these predicted fractions are in excellent agreement with available observations . 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 , probably because our simulated temperature profiles are flat or rising towards small radii while observed profiles decline at r \lesssim 0.2 R _ { vir } . 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 . Improved simulations and observations are needed to understand the remaining discrepancies and to decide the relative importance of cooling and non-gravitational heating in determining X-ray scalings .