Title: Fossil Groups and their luminosity functions Author(s): L. Sodre Jr., R. Lopes de Oliveira, C. Mendes de Oliveira, E. Cypriano, R. Dupke, D. R. Bortoletto Abstract: Fossil Groups are groups (or clusters) of galaxies optically dominated by an elliptical galaxy immersed in an extended and luminous X-ray halo, in which the magnitude gap between the two brightest galaxies within half of the virial radius is greater than 2 in the r-band. Recent studies suggest that the central galaxies in Fossil Groups are most likely formed by mergers of galaxies that had lost energy by dynamical friction, and that the velocity dispersion and X-rays properties of these systems are reminiscent of those of clusters, more than groups of galaxies. Here we report on the results of our search for new fossil groups and confirmation of candidates suggested in the literature by acquiring spectroscopy with Gemini/GMOS of the member galaxies. We also present a photometric study of the luminosity function of a sample of 10 group candidates using the SDSS database. A Schechter function describes well the individual luminosity functions, with an alpha parameter ranging from 0.5 to -1.5. Our fossil groups have a range of masses and other properties ranging from groups to clusters.