Long duration gamma-ray bursts (GRBs) and broad-line, type Ic supernovae (SNe) are strongly connected. We aim at characterizing SN 2013dx, associated with GRB,130702A, through sensitive and extensive ground-based observational campaigns in the optical-IR band. We monitored the field of the Swift GRB 130702A (redshift z = 0.145) using the 8.2-m VLT, the 3.6-m TNG and the 0.6-m REM telescopes during the time interval between 4 and 40 days after the burst. Photometric and spectroscopic observations revealed the presence of the associated Type Ic SN 2013dx. Our multi-band photometry allowed the construction of a bolometric light curve.} The bolometric light curve of SN 2013dx resembles that of 2003dh (associated with GRB 030329), but is ~10% faster and ~25% dimmer. From this we infer a synthesized 56Ni mass of ~0.2 solar masses. The multi-epoch optical spectroscopy shows that the SN 2013dx behavior is best matched by SN 1998bw, among the other well-known low-redshift SNe associated with GRBs and XRFs, and by SN 2010ah, an energetic Type Ic SN not associated with any GRB. The photospheric velocity of the ejected material declines from ~2.7X10^4 km/s at 8 rest frame days from the explosion, to ~3.5X10^3 km/s at 40 days. These values are extremely close to those of SN1998bw and 2010ah. We deduce for SN 2013dx a kinetic energy of ~35X10^51 erg, and an ejected mass of ~7 solar masses. This suggests that the progenitor of SN2013dx had a mass of ~25 solar masses, i.e., 15-20% less massive than that of SN 1998bw. Finally, we performed a study of the SN 2013dx environment, through spectroscopy of the closeby galaxies. 9 out of the 14 inspected galaxies lie within 0.03 in redshift from z=0.145, indicating that the host of GRB 130702A/SN 2013dx belongs to a group of galaxies, an unprecedented finding for a GRB-associated SN and, to our knowledge, for long GRBs in general.
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