Independence of Yoshikawa eighth move and a minimal generating set of band moves

Yoshikawa moves were introduced at least quarter-century ago and are still actively used by researchers. For any marked graph diagram we will define its twisted diagram and its mirror cut surface. By using a surface-link group of a mirror cut surface of a twisted diagram we will prove the independence of Yoshikawa eighth move. As a consequence we will establish a minimal generating set of band moves for links with bands.