We perform numerical simulations on the merger of multiple black holes (BHs) in primordial gas at early cosmic epochs. We consider two cases of BH mass: $M_{BH} = 30 M_{odot}$ and $M_{BH} = 10^4 M_{odot}$. Attention is concentrated on the effect of the dynamical friction by gas in a host object. The simulations incorporate such general relativistic effects as the pericentre shift and gravitational wave emission. As a result, we find that multiple BHs are able to merge into one BH within 100 Myr in a wide range of BH density. The merger mechanism is revealed to be categorized into three types: gas-drag-driven merger (type A), interplay-driven merger (type B), and three-body-driven merger (type C). We find the relation between the merger mechanism and the ratio of the gas mass within the initial BH orbit ($M_{gas}$) to the total BH mass (${Sigma}M_{BH}$). Type A merger occurs if $M_{gas} gtrsim 10^5 {Sigma}M_{BH}$, type B if $M_{gas} lesssim 10^5 {Sigma}M_{BH}$, and type C if $M_{gas} ll 10^5 {Sigma}M_{BH}$. Supposing the gas and BH density based on the recent numerical simulations on first stars, all the BH remnants from first stars are likely to merge into one BH through the type B or C mechanism. Also, we find that multiple massive BHs ($M_{BH} = 10^4 M_{odot}$) distributed over several parsec can merge into one BH through the type B mechanism, if the gas density is higher than $5times 10^6$ cm$^{-3}$. The present results imply that the BH merger may contribute significantly to the formation of supermassive BHs at high redshift epochs.
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