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

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