  Among the multiple stellar populations in globular clusters (GCs) the very
high-temperature H-burning regime, able to produce elements up to potassium, is
still poorly explored. Here we present the first abundance analysis of K in 42
giants of NGC 6715 (M 54) with homogeneous abundances of light elements
previously derived in our FLAMES survey. Owing to the large mass and low
metallicity, a large excess of K could be expected in this GC, which is located
in the nucleus of the Sagittarius dwarf galaxy. We actually found a spread in
[K/Fe] spanning about 1 dex, with [K/Fe] presenting a significant
anti-correlation with [O/Fe] ratios, regardless of the metallicity component in
M 54. Evidence for a K-Mg anti-correlation also exists, but this is
statistically marginal because of the lack of very Mg-poor stars in this GC. We
found, however, a strong correlation between K and Ca. These observations
clearl y show that the K enhancement in M 54 is probably due to the same
network of nuclear reactions generating the phenomenon of multiple stellar
populations, at work in a regime of very high temperature. The comparison with
recent results in omega Cen is hampered by an unexplained trend with the
temperatures for K abundances from optical spectroscopy, and somewhat by a
limited sample size for infrared APOGEE data. There are few doubts, however,
that the two most massive GCs in the Milky Way host a K-Mg anti-correlation.
