We study galaxies drawn from the semi-analytic models of Guo et al. (2011) based on the Millennium Simulation. We establish a set of four observationally measurable parameters which can be used in combination to identify a subset of galaxy groups which are old, with a very high probability. We therefore argue that a sample of fossil groups selected based on the luminosity gap will result in a contaminated sample of old galaxy groups. By adding constraints on the luminosity of the brightest galaxy, and its offset from the group luminosity centroid, we can considerably improve the age-dating.

We use the millennium simulation for studying the evolution of groups of galaxies over time. We find fossil and non-fossil groups as well as old and young groups at redshift z = 0 and follow them back in time to investigate the evolution of their parameters, such as mass assembly, luminosity gap and halo mass concentration. We find that fossils assemble a larger fraction of their mass at z = 0 than controls. The magnitude gaps between fossil and non-fossil groups are not the same because of major and minor mergers, in old and young groups as well. We also find that WMAP1 and WMAP7 cosmologies lead to the same evolutionary history for fossil and control groups.

We use multi-wavelength observations of galaxy groups to probe the formation models for galaxy for- mation in cosmological simulations, statistically. The observations include Chandra and XMM-Newton X-ray observations, optical photometry and radio observations at 1.4 GHz and 610 MHz. Using a large sample of galaxy groups observed by the XMM-Newton X-ray telescope as part of the XMM-Large Scale Survey, we carried out a statistical study of the redshift evolution of the luminosity gap for a well de- fined mass-selected group sample and show the relative success of some of the semi-analytic models in reproducing the observed properties of galaxy groups up to redshift z ~ 1.2. The observed trend argues in favour of a stronger evolution of the feedback from active galactic nuclei at z < 1 compared to the models. The slope of the relation between the magnitude of the brightest cluster galaxy and the value of the luminosity gap does not evolve with redshift and is well reproduced by the models. We find that the radio power of giant elliptic galaxies residing in galaxy groups with a large luminosity gap are lower compared to giant ellipticals of the same stellar masses but in typical galaxy groups.