In short period pseudodirect GaAs/AlAs superlattices, the two radiative heavy exciton states exhibit a very small anisotropic splitting due to their coupling with light exciton states. They are dipole-active along the [110] and [1(-1)0] directions in the layer plane. The splitting energy (a few µeV) is obtained from the period of the quantum beats between the two sublevels observed during the time decay of photoluminescence under excitation with light linearly polarized along [101] or circularly polarized. We report here on the variation of the quantum beats in a magnetic field. In a longitudinal field (parallel to the wave vector of light), we measure the splitting between the radiative states and obtain the hole longitudinal g-factor. In a transverse field, we observe two periods for the quantum beats. One corresponds to the splitting between the radiative states and the other to the splitting between the radiative states and the non-radiative ones which become optically allowed in a transverse field. We also discuss the influence of the coupling to light excitons in a transverse field on the hole transverse g-factor.