All boards of trustees of public high schools shall prohibit fraternities, sororities, or secret societies in all high schools under their respective jurisdiction. It shall be the duty of said boards of trustees to suspend or expel from said high schools under their control, any pupil or pupils who shall be or remain a member of, or shall join or promise to join, or who shall become pledged to become a member, or who shall solicit or encourage any other person to join, promise to join, or be pledged to become a member of, any such public high school fraternity, sorority or secret society, as defined in Section 37-11-37.