  Many of the satellites of galactic-mass systems such as the Miky Way,
Andromeda and Centaurus A show evidence of coherent motions to a larger extent
than most of the systems predicted by the standard cosmological model. It is an
open question if correlations in satellite orbits are present in systems of
different masses. Here , we report an analysis of the kinematics of satellite
galaxies around massive galaxy groups. Unlike what is seen in Milky Way
analogues, we find an excess of diametrically opposed pairs of satellites that
have line-of-sight velocity offsets from the central galaxy of the same sign.
This corresponds to a $\pmb{6.0\sigma}$ ($\pmb{p}$-value $\pmb{=\
9.9\times10^{-10}}$) detection of non-random satellite motions. Such excess is
predicted by up-to-date cosmological simulations but the magnitude of the
effect is considerably lower than in observations. The observational data is
discrepant at the $\pmb{4.1\sigma}$ and $\pmb{3.6\sigma}$ level with the
expectations of the Millennium and the Illustris TNG300 cosmological
simulations, potentially indicating that massive galaxy groups assembled later
in the real Universe. The detection of velocity correlations of satellite
galaxies and tension with theoretical predictions is robust against changes in
sample selection. Using the largest sample to date, our findings demonstrate
that the motions of satellite galaxies represent a challenge to the current
cosmological model.
