The fragmentation of a molecular cloud that leads to the formation of high-mass stars occurs on a hierarchy of different spatial scales. The large molecular clouds harbour massive molecular clumps with massive cores embedded in them. The fragmentation of these cores may determine the initial mass function and the masses of the final stars. Therefore, studying the fragmentation processes in the cores is crucial to understand how massive stars form. The hot molecular core G34-MM1, embedded in IRDC G34.34+00.24 located at a distance of 3.6 kpc, is a promising object to study both the fragmentation and outflow processes. Using data at 93 and 334 GHz obtained from the Atacama Large Millimeter Array (ALMA) database we studied G34-MM1 with great detail. The angular resolution of the data at 334 GHz allowed us to resolve structures of about 0.014 pc ($sim$2900 au). We found evidence of fragmentation towards the molecular hot core G34-MM1 at two different spatial scales. The dust condensation MM1-A (about 0.06 pc in size) harbours three molecular subcores candidates (SC1 through SC3) detected in $^{12}$CO J=3-2 emission, with typical sizes of about 0.02 pc. From the HCO$^+$ J=1-0 emission, we identify, with better angular resolution than previous observations, two perpendicular molecular outflows arising from MM1-A. We suggest that subcores SC1 and SC2, embedded in MM1-A, harbour the sources responsible of the main and the secondary molecular outflow, respectively. Finally, from the radio continuum emission at 334 GHz, we marginally detected another dust condensation, named MM1-E, from which a young, massive, and energetic molecular outflow arises. The fragmentation of the hot molecular core G34-MM1 at two different spatial scales, together with the presence of multiple molecular outflows associated with it, would support a competitive accretion scenario.
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