  The abundance of galaxy clusters as a function of mass is determined using
the 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue. This is used to
estimate the amplitude of the matter fluctuation spectrum, parametrised by the
linear theory rms density fluctuations in spheres of 8Mpc/h, sigma_8. The
best-fitting value for this parameter is highly correlated with the mean matter
density in the Universe, Omega_m, and is found to satisfy
sigma_8=0.25Omega_m^{-0.92-4.5(Omega_m-0.22)^2}+/-10%(statistical)+/-20%
(systematic) for 0.18<Omega_m<0.50, assuming that Omega_m+Omega_Lambda=1. This
gives sigma_8=0.89 when Omega_m=0.25. A ~20% correction has been applied to
undo the systematic bias inherent in the measurement procedure. Mock
catalogues, constructed from large cosmological N-body simulations, are used to
help understand and model these systematic errors. The abundance of galaxy
groups as a function of group bj band luminosity is also determined. This is
used in conjunction with the halo mass function, determined from simulations,
to infer the variation of halo mass-to-light ratio over four orders of
magnitude in halo mass. The mass-to-light ratio shows a minimum value of
100hM_sol/L_sol in the bj band at a total group luminosity of L_bJ ~
5.10^9Lsol/h^2. Together with the observed Tully-Fisher relation, this implies
that the observed rotation speed of Tully-Fisher galaxies is within ~10% of the
typical circular speed of haloes hosting brightest galaxies of the same
luminosity.
