The reaction 9Be(28Mg,26Ne+gamma)X has been studied at 82 MeV/nucleon together with two similar cases, 30Mg and 34Si. Strong evidence that the reactions are direct is offered by the parallel-momentum distributions of the reaction residues and by the inclusive cross sections. The pattern of the partial cross sections for 28Mg suggests the presence of correlations. A preliminary theoretical discussion based on eikonal reaction theory and the many-body shell model is presented. The reaction holds great promise for the study of neutron-rich nuclei.