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Using galaxy groups identified in the Fourth Data Release of the SloanDigital Sky Survey (SDSS), we compute the luminosity function for severalsubsamples of galaxies in groups. In all cases, the luminosity functions arewell described by Schechter functions, down to the faintest magnitudes weprobe, $M_{\rb}-5\log(h)\sim-16$. For the general luminosity function ofgalaxies in groups in the five SDSS bands, we observe that the characteristicmagnitude is brighter in $\sim 0.5$ magnitudes compared to those obtained forfield galaxies by Blanton et al.. Even when the observed faint end slope issteeper in galaxy groups, it is statistically comparable with the field value.We analyze the dependence of the galaxy luminosity function with system massesfinding two clear trends: a continuous brightening of the characteristicmagnitude and a steepening of the faint end slope as mass increases. Theresults in $\gb$, $\rb$, $\ib$ and $\zb$ bands show the same behavior. Usingthe $u-r$ color to split the galaxy sample into red and blue galaxies, we showthat the changes observed as a function of the system mass are mainly seen inthe red, passively evolving, galaxy population, while the luminosities of bluegalaxies remain almost unchanged with mass. Finally, we observe that groupshaving an important luminosity difference between the two brightest galaxies ofa system show a steeper faint end slope than the other groups. Our results canbe interpreted in terms of galaxy mergers as the main driving force behindgalaxy evolution in groups.Comment: 29 pages, 10 figures, submitted to Astrophysical Journa

On the Luminosity Function of Galaxies in Groups in the Sloan Digital Sky Survey