  Geometrically thick tori with constant specific angular momentum have been
widely used in the last decades to construct numerical models of accretion
flows onto black holes. Such discs are prone to a global non-axisymmetric
hydrodynamic instability, known as Papaloizou-Pringle instability (PPI), which
can redistribute angular momentum and also lead to an emission of gravitational
waves. It is, however, not clear yet how the development of the PPI is affected
by the presence of a magnetic field and by the concurrent development of the
magnetorotational instability (MRI). We present a numerical analysis using
three-dimensional GRMHD simulations of the interplay between the PPI and the
MRI considering, for the first time, an analytical magnetized equilibrium
solution as initial condition. In the purely hydrodynamic case, the PPI selects
as expected the large-scale $m=1$ azimuthal mode as the fastest growing and
non-linearly dominant mode. However, when the torus is threaded by a weak
toroidal magnetic field, the development of the MRI leads to the suppression of
large-scale modes and redistributes power across smaller scales. If the system
starts with a significantly excited $m=1$ mode, the PPI can be dominant in a
transient phase, before being ultimately quenched by the MRI. Such dynamics may
well be important in compact star mergers and tidal disruption events.
