We derive composite luminosity functions (LF) for galaxies in groups and examine the behavior of the LF as a function of group luminosity (used as an indicator of group or halo mass). We consider both the entire galaxy population and galaxies split into red and blue (quiescent and star-forming) samples, in order to examine possible mechanisms behind observed variations of galaxy properties with environment. We find evidence that M* brightens and α steepens with group luminosity, until a threshold value where the LF parameters stabilize at those found in rich clusters. The effect is seen in the total LF and for the blue and red galaxies separately. The behavior of the quiescent and star-forming samples is qualitatively consistent with variations resulting from interactions and mergers, where mergers build the bright end of the luminosity function at the same time as dwarf irregulars have their star formation quenched and evolve into dwarf ellipticals. These processes appear to take place preferentially in low-luminosity groups and to be complete at a group luminosity of -22.5 in B, corresponding to a halo mass of order 10 13.5 M⊙.