  We present techniques for identifying and analyzing galaxy groups and show
that they provide a powerful discriminator between cosmological models. We
apply these to high-resolution PM N-body simulations of structure formation in
CHDM (cold/hot/baryon fractions=.6/.3/.1, b=1.5 (COBE norm) and two CDM models;
b=1.5 and b=1.0 (COBE norm). Groups are identified with the Nolthenius (1993)
algorithm. We find: (1) Properties of groups are a powerful and robust
discriminator between these Gaussian models whose spatial and velocity
properties differ on Mpc scales. We test robustness against several methods for
assigning luminosity to dark matter halos, for merging CfA1 galaxies, and for
breaking up massive over-mergers (2) When allowance is made for the high large
scale power P(k) present in the CfA1 data, CHDM at our $\Omnu=0.30$ produces
slightly too many groups and groups too high a fraction of the galaxies, while
the fraction grouped in CDM is far too low. Lowering $\Omnu$ would appear to
produce close agreement with all measures, save one: for all simulations,
median group sizes are x1.4-1.7 larger than equivalently selected CfA1 groups.
(3) The standard group M/L method gives $\Omega\simeq 0.1$ for CHDM and CfA1,
and $\Omega\simeq 0.35$ for CDM. A conspiracy of three effects produce these
very low values, and we conclude that low observed $\Omega$'s need not argue
for a low $\Omega$ universe. When overmergers are broken up, the median virial-
to-DM mass of 3D selected groups is $\sim1$ for all simulations.
$M_{DM}>10^{14}\Msun$ groups appear virialized in all simulations. Global
velocity biases $b_v$ are similar to previous studies. Within 3D-selected
groups, CHDM and CDM b=1.5 show a stronger bias of $b_v=0.7-0.8$, while CDM
b=1.0 shows group $b_v$'s $\simeq 1$.
