We create a catalogue of simulated fossil groups and study their properties, in particular the merging histories of their first-ranked galaxies. We compare the simulated fossil group properties with those of both simulated non-fossil and observed fossil groups. Using simulations and a mock galaxy catalogue, we searched for massive ($>$ 5 $times$ 10$^{13} h^{-1} {cal M}_odot$) fossil groups in the Millennium Simulation Galaxy Catalogue. In addition, attempted to identify observed fossil groups in the Sloan Digital Sky Survey Data Release 6 using identical selection criteria. Our predictions on the basis of the simulation data are:(a) fossil groups comprise about 5.5% of the total population of groups/clusters with masses larger than 5 x 10$^{13} h^{-1} {cal M}_odot$. This fraction is consistent with the fraction of fossil groups identified in the SDSS, after all observational biases have been taken into account; (b) about 88% of the dominant central objects in fossil groups are elliptical galaxies that have a median R-band absolute magnitude of $sim -23.5-5 log h$, which is typical of the observed fossil groups known in the literature; (c)first-ranked galaxies of systems with $ {cal M} >$ 5 x 10$^{13} h^{-1} {cal M}_odot$, regardless of whether they are either fossil or non-fossil, are mainly formed by gas-poor mergers; (d) although fossil groups, in general, assembled most of their virial masses at higher redshifts in comparison with non-fossil groups, first-ranked galaxies in fossil groups merged later, i.e. at lower redshifts, compared with their non-fossil-group counterparts. We therefore expect to observe a number of luminous galaxies in the centres of fossil groups that show signs of a recent major merger.
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