  The linear stability of MHD Taylor-Couette flow of infinite vertical
extension is considered for various magnetic Prandtl numbers Pm. The
calculations are performed for a wide gap container with \hat\eta=0.5 with an
axial uniform magnetic field excluding counterrotating cylinders. For both
hydrodynamically stable and unstable flows the magnetorotational instability
produces characteristic minima of the Reynolds number for certain (low)
magnetic field amplitudes and Pm> 0.01. For Pm <~ 1 there is a characteristic
magnetic field amplitude beyond which the instability sets in in form of
nonaxisymmetric spirals with the azimuthal number m=1. Obviously, the magnetic
field is able to excite nonaxisymmetric configurations despite of the tendency
of differential rotation to favor axisymmetric magnetic fields which is known
from the dynamo theory. If Pm is too big or too small, however, the
axisymmetric mode with m=0 appears to be the most unstable one possessing the
lowest Reynolds numbers -- as it is also true for hydrodynamic Taylor-Couette
flow or for very weak fields. That the most unstable mode for modest Pm proves
to be nonaxisymmetric must be considered as a strong indication for the
possibility of dynamo processes in connection with the magnetorotational
instability.
