  \def\spose#1{\hbox to 0pt{#1\hss}} \def\lta{\mathrel{\spose{\lower
3pt\hbox{$\mathchar"218$}}
  \raise 2.0pt\hbox{$\mathchar"13C$}}} Groups of galaxies are highly linked to
cosmology: 1) groups are tidally destroyed by the tidal field of the cluster
they fall into; 2) spherical infall leads to the young cosmo-dynamical state of
loose groups, a fundamental surface for groups, $\Omega_0 \simeq 0.3$, and the
mixed nature of compact groups (virialized groups, groups at full collapse, and
chance alignments within collapsing loose groups, for decreasing compact group
velocity dispersion) ; 3) X-ray analyses lead to $\Omega_0 \lta 0.5$.
