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We study the merger history of primordial black holes (PBHs) in a scenariowhere they represent the dominant dark matter component of a typical dwarfgalaxies' core. We investigate the possibility of a sequence of collisionsresulting in a hierarchical merger of black holes and look at the final massspectrum in such {\it clusters}, which initially present a monochromatic(single-mass) PBH population. Our study shows that the merging process resultsin the transfer of about $40\%$ of the total mass of the core to the mergerproducts regardless of the initial mass of PBHs, with about $5\%$ of energyradiated out in the form of gravitational waves. We find that, in the lightermass limit, black holes up to eight times more massive than the originalpopulation can be formed within a Hubble time.

Hierarchical Merger of Primordial Black Holes in Dwarf Galaxies