We present the results of a search for galaxy clusters and groups in the ˜2 deg2 of the COSMOS field using all available X-ray observations from the XMM-Newton and Chandra observatories. We reach an X-ray flux limit of 3× 10^{-16} erg cm^{-2 s}^{-1} in the 0.5-2 keV range, and identify 247 X-ray groups with M_{ 200c}=8× 10^{12}-3× 10^{14} M_{⊙} at a redshift range of 0.08 ≤ z < 1.53, using the multiband photometric redshift and the master spectroscopic redshift catalogues of the COSMOS. The X-ray centres of groups are determined using high-resolution Chandra imaging. We investigate the relations between the offset of the brightest group galaxies (BGGs) from halo X-ray centre and group properties and compare with predictions from semi-analytic models and hydrodynamical simulations. We find that BGG offset decreases with both increasing halo mass and decreasing redshift with no strong dependence on the X-ray flux and SNR. We show that the BGG offset decreases as a function of increasing magnitude gap with no considerable redshift-dependent trend. The stellar mass of BGGs in observations extends over a wider dynamic range compared to model predictions. At z < 0.5, the central dominant BGGs become more massive than those with large offsets by up to 0.3 dex, in agreement with model prediction. The observed and predicted log-normal scatter in the stellar mass of both low- and large-offset BGGs at fixed halo mass is ˜0.3 dex.
