As part of our on-going project on the homogeneous chemical characterization of multiple stellar populations in globular clusters (GCs), we studied NGC 5634, associated to the Sagittarius dwarf spheroidal galaxy, using high-resolution spectroscopy of red giant stars collected with FLAMES@VLT. We present here the radial velocity distribution of the 45 observed stars, 43 of which are member, the detailed chemical abundance of 22 species for the seven stars observed with UVES-FLAMES, and the abundance of six elements for stars observed with GIRAFFE. On our homogeneous UVES metallicity scale we derived a low metallicity [Fe/H]=-1.867 +/-0.019 +/-0.065 dex (+/-statistical +/-systematic error) with sigma=0.050 dex (7 stars). We found the normal anti-correlations between light elements (Na and O, Mg and Al), signature of multiple populations typical of massive and old GCs. We confirm the associations of NGC 5634 to the Sgr dSph, from which the cluster was lost a few Gyr ago, on the basis of its velocity and position and the abundance ratios of alpha and neutron capture elements.
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