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.

ABSTRACT
1. INTRODUCTION
2. THE DATA AND THE SIMULATIONS
3. LUMINOSITY GAP STATISTICS
4. LUMINOSITY FUNCTION
5. FUTURE GALAXY MODELLING; CONSTRAINTSON AGN ACTIVITIES
REFERENCES

• Habib. G. Khosroshahi(School of Astronomy, Institute for Research in Fundamental Sciences)
• Ghassem Gozaliasl(School of Astronomy, Institute for Research in Fundamental Sciences/Department of Physics, University of Helsinki)
• Alexis Finoguenov(Department of Physics, University of Helsinki)
• Mojtaba Raouf(School of Astronomy, Institute for Research in Fundamental Sciences)
• Halime MirAghee(School of Astronomy, Institute for Research in Fundamental Sciences)