Magnetized inertial fusion (MIF) could substantially ease the difficulty of reaching plasma conditions required for significant fusion yields, but it has been widely accepted that the gain is not sufficient for fusion energy. Numerical simulations are presented showing that high-gain MIF is possible in cylindrical liner implosions based on the MagLIF concept [S. A. Slutz et al Phys. Plasmas 17, 056303 (2010)] with the addition of a cryogenic layer of deuterium-tritium (DT). These simulations show that a burn wave propagates radially from the magnetized hot spot into the surrounding much denser cold DT given sufficient hot-spot areal density. For a drive current of 60 MA the simulated gain exceeds 100, which is more than adequate for fusion energy applications. The simulated gain exceeds 1000 for a drive current of 70 MA.