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While it is possible that other symmetry breaking mechanisms like rapid rotation could play a role similar to a strong magnetic field, we believe this is an unlikely explanation for the bulk of the suppressed dipoles sample (see details in the supplementary material). This is because the rotation rate required to modify the incoming waves such that they will be trapped in the core, is two orders of magnitude higher than the values commonly observed in the cores of these stars \citep{Beck_2011,Mosser_2012}. Moreover the magnetic greenhouse effect makes a clear prediction: that for stars with frequency of maximum power similar to the critical magneto gravity frequency $\nu_{\rm c}$, dipole modes with $\nu >\nu_{\rm c}$ will be unaffected, while those with $\nu <\nu_{\rm c}$ should show suppression. The early subgiant star KIC 8561221 displays this exact behavior \citep{Garcia_2014}, demonstrating the reality of the magnetic greenhouse effect.  For the magnetic greenhouse effect to operate, stars need to have magnetic fields with a radial component $B\gtrsim 10^4 {\rm G}$ around the location of the H-burning shell. We note that magnetic fields of similar amplitude have been discussed in order to explain the suppression of thermohaline mixing in a small fraction of red giant stars, as inferred from the observations of their surface abundances \cite{Charbonnel_2007}.  Magnetic fields with these characteristics could be present if the star retained a fossil field with surface amplitude $\sim 1 {\rm kG}$ on the main sequence, or if a convective core dynamo was at work during the main sequence (equipartition (sub-equipartition  magnetic fields are easily above $B \sim 10^4 {\rm G}$). The fraction of stars showing suppressed dipole modes in the data of \citet{Mosser_2011} is about 22\%, tentatively showing that red giants with magnetized cores are not just the descendants of Ap stars. A detailed analysis of a large population of red giants with suppressed dipole modes will put strong constraints on the amplitude and evolution of internal magnetic fields in stars of different mass (Stello et al. In prep.).  The asteroseismic technique described in this paper can also be applied to stars burning He in their cores. Observations of dipolar modes in clump stars will put important constraints on the internal magnetic field of the immediate progenitors of white dwarfs (AuthorX et al. In prep.).