Reaction cross sections (sigma R) for Mg24-38 on C targets at the energies of around 240 MeV/nucleon have been measured precisely at RIBF, RIKEN for the purpose of obtaining the crucial information on the changes of nuclear structure in unstable nuclei, especially around the so-called "island of inversion" region. In the island of inversion region, which includes neutron-rich Ne, Na, and Mg isotopes, the vanishing of the N = 20 magic number for neutrons have been discussed along with nuclear deformation. The present result suggest deformation features of Mg isotopes and shows a large cross section of weakly-bound nucleus Mg-37, which could be caused by a neutron halo formation.