A detailed transmission electron microscopy study is performed on the pyramidal inversion domains that appear in highly Mg-doped GaN grown by metalorganics vapor phase epitaxy or by the high-pressure, high-temperature method. From a comparison between high resolution images of the inversion domain boundaries and simulations using different atomic models, we conclude that both basal and inclined domain boundaries are likely formed of a monomolecular layer of the definite compound Mg3N2. We show that, due to their high concentration, the formation of these defects may account for auto-compensation in Mg-doped GaN. We also show that the local band bending induced by the polarity inversion due to these defects can be at the origin of the blue luminescence of highly Mg-doped GaN, always observed when nanometric pyramidal inversion domains are also present.