  We present N-body simulations of groups of galaxies with a number of very
different initial conditions. These include spherical isotropic, nonspherical
anisotropic collapses and virialised spherical systems. In all cases but one
the merging instability leads to the formation of a giant central galaxy in the
center of the group. The initial conditions of the exception are such that no
galaxies are present in the central part of the group. Thus some central seed
of material is necessary to trigger the formation of a giant central galaxy. We
concentrate on the properties of these giant central galaxies. Spherical
virialised systems give rise to relatively round and isotropic systems, while
aspherical initial conditions give rise to triaxial objects with anisotropic
velocity dispersion tensors. In the latter cases the orientation of the
resulting central galaxy is well correlated with that of the initial cluster.
We compare the projected properties of the objects formed with the properties
of real brightest cluster member galaxies. The surface density profiles are in
good agreement with the observed surface brightness profiles. In the case of
extended virialised groups the projected properties of the giant central galaxy
are the same as the properties of cD galaxies. These include a halo of luminous
material and a nearly flat velocity dispersion profile.
