  Recent work has shown that both the Milky Way and the Andromeda galaxies
possess the unexpected property that their dwarf satellite galaxies are aligned
in thin and kinematically coherent planar structures. It is now important to
evaluate the incidence of such planar structures in the larger galactic
population, since the Local Group may not be a sufficiently representative
environment. Here we report that the measurement of the velocity of pairs of
diametrically opposed galaxy satellites provides a means to determine
statistically the prevalence of kinematically coherent planar alignments. In
the local universe (redshift $z<0.05$), we find that such satellite pairs out
to a galactocentric distance of $150$ kpc are preferentially anti-correlated in
their velocities (99.994% confidence level), and that the distribution of
galaxies in the larger scale environment (beyond 150 kpc and up to $\approx 2$
Mpc) is strongly elongated along the axis joining the inner satellite pair
($>7\sigma$ confidence). Our finding may indicate that co-rotating planes of
satellites, similar to that seen around the Andromeda galaxy, are ubiquitous in
nature, while their coherent motion also suggests that they are a significant
repository of angular momentum on $\sim 100$ kpc scales.
