We use a set of 12 high-resolution N-body/hydrodynamical simulations in the ACDM cosmology to investigate the origin and formation rate of fossil groups (FGs), which are X-ray-bright galaxy groups dominated by a large elliptical galaxy, with the second brightest galaxy being at least 2 mag fainter. The simulations invoke star formation, chemical evolution with noninstantaneous recycling, metal-dependent radiative cooling, strong star-burst-driven galactic superwinds, effects of a metagalactic UV field, and full stellar population synthesis. We find an interesting correlation between the magnitude gap between the brightest and second-brightest galaxy and the formation time of the group. It is found that FGs have already assembled half of their final dark matter mass at z approx> 1, and subsequently they typically grow by minor merging only, whereas non-FGs on average form later. The early assembly of FGs leaves sufficient time for galaxies of L ～ L_* to merge into the central one by dynamical friction, resulting in the large magnitude gap at z = 0. About 33% ± 16% of the groups simulated are found to be FGs, whereas the observational estimate is ～10%-20%. The FGs are found to be overluminous in the X-ray relative to non-FGs of the same optical luminosity, in qualitative agreement with observations. Finally, from a dynamical friction analysis, we find that FGs exist at all only because infall of L ～ L_* galaxies happens along filaments with small impact parameters.
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