Experiments have shown that a cylindrical liner can successfully confine a magnetized, hot plasma column. The technical parameters necessary for ICF applications being inaccessible so far, we have investigated volume and spark ignition in a D-T plasma compressed by an imploding liner through numerical simulations. These calculations provide an insight into the structure of both the liner and the plasma and indicate the range of parameters required for ignition and detonation in such a liner-pinch system. Typical results, corresponding to physically feasible situations will be shown and means for realising them will be mentioned. Extrapolation to advanced fuels will be briefly outlined.