It has been a long-standing question whether fossil groups just sample the tail of the distribution of ordinary groups or whether they are a physically distinct class of objects, characterized by an unusual and special formation history. To answer this question, we here investigate fossil groups identified in the hydrodynamical simulations of the Galaxies Intergalactic Medium Interaction Calculation (GIMIC) project, which consists of resimulations of five regions in the Millennium Simulation (MS) that are characterized by different large-scale densities, ranging from a deep void to a proto-cluster region. For comparison, we also consider semi-analytic models built on top of the MS, as well as a conditional luminosity function approach. We identify galaxies in the GIMIC simulations as groups of stars and use a spectral synthesis code to derive their optical properties. The X-ray luminosity of the groups is estimated in terms of the thermal bremsstrahlung emission of the gas in the host haloes, neglecting metallicity effects. We focus on comparing the properties of fossil groups in the theoretical models and observational results, highlighting the differences between them and try to identify possible dependences on environment for which our approach is particularly well set up. We find that the optical fossil fraction in all of our theoretical models declines with increasing halo mass, and there is no clear environmental dependence. Combining the optical- and X-ray-selection criteria for fossil groups, the halo mass dependence of the fossil groups seen in optical vanishes. Over the GIMIC halo mass range, 9.0 × 1012-4.0 × 1013 h-1 M⊙, we resolve best that the central galaxies in the fossil groups show similar properties as those in ordinary groups in terms of age, metallicity, colour, concentration and mass-to-light ratio. And finally, the satellite galaxy number distribution of fossil groups is consistent with that of non-fossil groups. These results support an interpretation of fossil groups as transient phases in the evolution of ordinary galaxy groups rather than forming a physically distinct class of objects.
