Star formation in the centers of galaxies is thought to yield massive stars with a possibly top-heavy stellar mass distribution. It is likely that magnetic fields play a crucial role in the distribution of stellar masses inside star-forming molecular clouds. In this context, we explore the effects of magnetic fields, with a typical field strength of 38 μG, such as in RCW 38, and a field strength of 135 μG, similar to NGC 2024 and the infrared dark cloud G28.34+0.06, on the initial mass function (IMF) near (=10 pc) a 107 solar mass black hole. Using these conditions, we perform a series of numerical simulations with the hydrodynamical code FLASH to elucidate the impact of magnetic fields on the IMF and the star-formation efficiency (SFE) emerging from an 800 solar mass cloud. We find that the collapse of a gravitationally unstable molecular cloud is slowed down with increasing magnetic field strength and that stars form along the field lines. The total number of stars formed during the simulations increases by a factor of 1.5-2 with magnetic fields. The main component of the IMF has a lognormal shape, with its peak shifted to sub-solar (=0.3 M·) masses in the presence of magnetic fields, due to a decrease in the accretion rates from the gas reservoir. In addition, we see a top-heavy, nearly flat IMF above ∼2 solar masses, from regions that were supported by magnetic pressure until high masses are reached. We also consider the effects of X-ray irradiation if the central black hole is active. X-ray feedback inhibits the formation of sub-solar masses and decreases the SFEs even further. Thus, the second contribution is no longer visible. We conclude that magnetic fields potentially change the SFE and the IMF both in active and inactive galaxies, and need to be taken into account in such calculations. The presence of a flat component of the IMF would be a particularly relevant signature for the importance of magnetic fields, as it is usually not found in hydrodynamical simulations.