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Surface magnetic fields are routinely measured in stars. However, internal magnetic fields are inaccessible to direct observations and very little is known about their amplitude, geometry and evolution. In this paper, we demonstrate that a strong magnetic field in the core of red giant stars can suppress the amplitude of dipolar oscillation modes. Suppressed dipolar modes are indeed observed in a significant fraction of ascending RGB stars. We interpret these as stars with strongly magnetized cores, and we place lower limits on the internal magnetic field strength in stars with suppressed dipolar modes. The inferred magnetic fields field strengths  indicate these stars are the descendants of magnetic Ap stars, or hosted a powerful core dynamo during the main sequence. The novel asteroseismic technique reported here allows for constraints on magnetic fields in the deep interiors of a large population of stars.