Cosmological ( \Lambda CDM ) TreeSPH simulations of the formation and evolution of twelve galaxy groups of virial mass \sim 10 ^ { 14 } M _ { \odot } have been performed . The simulations invoke star formation , chemical evolution with non-instantaneous recycling , metallicity dependent radiative cooling , strong star-burst driven galactic super-winds and effects of a meta-galactic UV field . The intra-group ( IG ) stars are found to contribute 12-45 % of the total group B-band luminosity at z =0 . The lowest fractions are found for groups with only a small difference between the R-band magnitudes of the first and second ranked group galaxy ( \Delta m _ { 12 ,R } \la 0.5 ) , the larger fractions are typical of “ fossil ” groups ( FGs , \Delta m _ { 12 ,R } \geq 2 ) . A similar conclusion is obtained from BVRIJK surface brightness profiles of the IG star populations . The IG stars in the 4 FGs are found to be older than the ones in the 8 “ normal ” groups ( nonFGs ) , on average by about 0.3-0.5 Gyr . The typical colour of the IG stellar population is B-R=1.4-1.5 , for both types of systems in good agreement with observations . The mean Iron abundance of the IG stars is slightly sub-solar in the central part of the groups ( r \sim 100 kpc ) decreasing to about 40 % solar at about half the virial radius . The IG stars are \alpha -element enhanced with a trend of [ O/Fe ] increasing with r and an overall [ O/Fe ] \sim 0.45Â dex , indicative of dominant enrichment from type II supernovae . The abundance properties are similar for both types of systems . The velocity distributions of the IG stars are , at r \ga 30 kpc , significantly more radially anisotropic for FGs than for the nonFGs ; this also holds for the velocity distributions of the group galaxies . This indicates that an important characteristic determining whether a group becomes fossil or not , apart from its formation time , as discussed by D ’ Onghia et al. , is the “ initial ” velocity distribution of the group galaxies . For FGs one can dynamically infer the ( dark matter dominated ) mass distribution of the groups all the way to the virial radius , from the kinematics of the IG stars or group galaxies . For the nonFGs this method overestimates the group mass at r \ga 200 kpc , by up to a factor of two at the virial radius . This is interpreted as FGs being , in general , more relaxed than nonFGs . Finally , FGs of the above virial mass should host \sim 500 planetary nebulae at projected distances between 100 and 1000 kpc from the first ranked galaxy . All results obtained appear consistent with the tidal stripping and merging scenario for the formation of FGs , put forward by D ’ Onghia et al .