Galaxy groups, CDM/CHDM cosmologies, and the value of Omega(0)

We present techniques for identifying and analyzing galaxy groups and apply them to large-scale particle-mesh (PM) N-body simulations of structure formation in three Omega(0)=1 cosmological models: cold plus hot dark matter (CHDM), with Omega(cold)=0.6, Omega(v)=0.3, and Omega(baryon)=0.1 at bias b=sigma(8)(-1)=1.5; and two cold dark matter (CDM) models, at bias b=1.5 and b=1.0. Groups are identified with the adaptive friends-of-friends algorithm of Nolthenius. Our most important conclusions follow. The standard group M/L method gives Omega(0) similar or equal to 0.08 for the CfA1 survey (for redshift link parameter V-5=350), and, applied to our Omega(0)=1 simulations, it gives Omega(0) similar or equal to 0.12 for CHDM (V-5=350) and Omega(0) similar or equal to 0.35 for CDM (V-5=600). This Omega bias appears to be even stronger at higher resolution. We show quantitatively how three different effects conspire to produce this large discrepancy, and we conclude that low observed Omega values need not argue for a low-Omega universe. Our preferred statistics of groups show promise in becoming powerful discriminators between Gaussian cosmological models, whose Omega(v) differ and are robust against several methods for assigning luminosity to dark matter halos, and for merging CfA1 data. However, our latest results at higher resolution show such strong sensitivity to how massive overmergers are broken up that more reliable ways of identifying luminous galaxies within large-scale simulations will be necessary before these statistics can provide reliable discrimination. When overmergers are broken up, the median virial-to-DM mass M-vir/M-DM of three-dimensional-selected groups is similar to 1 for all simulations. Groups with M-DM>10(14) M. appear virialized in all simulations. We measure global (not pairwise) velocity biases b(v), similar to previous studies. Within three-dimensional-selected groups, CHDM and CDM with b=1.5 show a stronger bias of b(v)=0.7-0.8, while CDM with b=1.0 shows groups of b(v) similar or equal to 1.