Galaxy groups in the 2dF galaxy redshift survey: Luminosity and Mass   Statistics
  Several statistics are applied to groups and galaxies in groups in the Two degree Field Galaxy Redshift Survey. Firstly we estimate the luminosity functions for different subsets of galaxies in groups. The results are well fitted by a Schechter function with parameters $M^{\ast}-5\log(h)=-19.90 \pm 0.03$ and $\alpha=-1.13\pm0.02$ for all galaxies in groups, which is quite consistent with the results by Norberg et al. for field galaxies. When considering the four different spectral types defined by Madgwick et al. we find that the characteristic magnitude is typically brighter than in the field. We also observe a steeper value, $\alpha=-0.76\pm 0.03$, of the faint end slope for low star-forming galaxies when compared with the corresponding field value. This steepening is more conspicuous, $\alpha=-1.10\pm 0.06$, for those galaxies in more massive groups (${\mathcal M} \gsim 10^{14} h^{-1} M_{\odot}$) than the obtained in the lower mass subset, $\alpha=-0.71\pm 0.04$ (${\mathcal M}<10^{14} h^{-1} M_{\odot}$). Secondly, we compute group total luminosities using Moore, Frenk & White prescriptions. We define a flux-limited group sample using a new statistical tool developed by Rauzy. The resulting group sample is used to determine the group luminosity function finding a good agreement with previous determinations and semianalytical models. Finally, the group mass function for the flux-limited sample is derived. An excellent agreement is obtained when comparing our determination with analytical predictions over two orders of magnitude in mass. 
H. J. Martinez, A. Zandivarez, M. E. Merchan & M.J.L. Dominguez (Grupo   de Investigaciones en Astronomia Teorica y Experime...