We report the discovery of a Multi Unit Spectroscopic Explorer (MUSE) galaxy group at z=4.32 lensed by the massive galaxy cluster ACT-CL J0102-4915 (aka El Gordo) at z=0.87, associated with a 1.2 mm source which is at a 2.07+/-0.88 kpc projected distance from one of the group galaxies. Three images of the whole system appear in the image plane. The 1.2 mm source has been detected within the Atacama Large Millimetre/submillimetre Array (ALMA) Lensing Cluster Survey (ALCS). As this ALMA source is undetected at wavelengths lambda < 2 microns, its redshift cannot be independently determined, however, the three lensing components indicate that it belongs to the same galaxy group at z=4.32. The four members of the MUSE galaxy group have low to intermediate stellar masses (~ 10^7-10^{10} Msun) and star formation rates (SFRs) of 0.4-24 Msun/yr, resulting in high specific SFRs (sSFRs) for two of them, which suggest that these galaxies are growing fast (with stellar-mass doubling times of only ~ 2x10^7 years). This high incidence of starburst galaxies is likely a consequence of interactions within the galaxy group, which is compact and has high velocity dispersion. Based on the magnification-corrected sub-/millimetre continuum flux density and estimated stellar mass, we infer that the ALMA source is classified as an ordinary ultra-luminous infrared galaxy (with associated dust-obscured SFR~200-300 Msun/yr) and lies on the star-formation main sequence. This reported case of an ALMA/MUSE group association suggests that some presumably isolated ALMA sources are in fact signposts of richer star-forming environments at high redshifts.
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