X-Ray and Optical Properties of Groups of Galaxies
  We examine the relationship between the group x-ray luminosity in the 0.3-3.5 keV band and the measured velocity dispersion, and galaxy surface number density. We find definite correlations. Richer groups follow the same relation as rich clusters (cf. Quintana & Melnick 1982) with $L_x \propto \sigma^{4.0\pm 0.6}$, but the relation flattens for lower luminosity systems which have velocity dispersions below 300 km/s). We suggest that the $L_x-\sigma$ relation arises from a combination of extended cluster emission and emission associated with individual galaxies. The x-ray emission for the richer groups is dominated by emission from the intra-group medium, as for the richer clusters; emission from the poorer clusters is dominated by less extended emission associated with the individual group galaxies. This is a corrected version of the paper which appeared in the Astronomical Journal (February 1994). We include a new version of the affected figure. 
I.P. Dell'Antonio, M.J. Geller, and D.G. Fabricant