  The linear marginal instability of an axisymmetric MHD Taylor-Couette flow of
infinite vertical extension is considered. The dependence of the flow stability
on magnetic Prandtl number, Pm, and gap-width between rotating cylinders is
investigated. There is an unstability for flows with resting outer cylinder
even without a magnetic field. Nevertheless, there are solutions with smaller
critical Reynolds numbers for certain (weak) magnetic fields. These solutions,
however, exist for not too small Pm or large enough gap. For hydrodynamically
stable flow, we found that a magnetic field amplitude always exsits where the
critical Reynolds number is minimal. In all calculated cases the minimal
critical Reynolds numbers are running with 1/Pm for small Pm and the critical
Reynolds numbers exceed value of 10^6 for Pm of sodium (10^{-5}) or gallium
(10^{-6}).
