We first present the results of numerical simulations on formation processes and physical properties of old globular clusters (GCs) located within clusters of galaxies (``intracluster GCs) and in between clusters of galaxies (``intercluster GCs). Our high-resolution cosmological simulations with models of GC formation at high redshifts ($z>6$) show that about 30 % of all GCs in a rich cluster can be ragarded as intracluster GCs that can freely drift being trapped by gravitational potential of the cluster rather than by the cluster member galaxies. The radial surface density profiles of the simulated intracluster GCs are highly likely to be flatter than those of GCs within cluster member galaxies. We also find that about 1% of all GCs formed before $z>6$ are not located within any virialized halos and can be regarded as ``intercluster (or ``intergalactic) GCs. We discuss the dependences of physical properties of intracluster and intercluster GCs on the initial density profiles of GCs within low-mass dark matter halos at high redshifts ($z>6$).
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