On the possibility of superconductivity in a MgB$_2$ compound

A concept of strong interaction in a single unit cell is used to predict Cooper instability in a system with hopping between main-group cations and anions. A phase diagram of ferromagnetic ordering is constructed for different degrees of ($(n_p)$ $p^6$- and $(n_s)s^{2}$-shell filling in main-group elements.