We performed a series of direct N-body simulations with the aim to follow the dynamical evolution of a galaxy cluster (GC) (\(M_{clus}\simeq 10^{14} M_{\odot}\)) in different environment. The results show the formation of heavy sub-structures in the cluster centre in consequence of multiple merging among the innermost galaxies. Moreover we investigate the dynamics of super-massive black holes (SMBHs) residing in the centre of galaxies that form the most massive sub-structure.
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