Massive black holes interactions during the assembly of heavy sub-structures in the centre of galaxy clusters

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.