Is it permissible to divorce a wife who left the marital home and traveled without her husband's knowledge, especially given that she previously admitted to committing indecency before marriage?

Wife-beating is not a wise action if it is not beneficial, and it must be preceded by admonition and non-violent abandonment. A wife leaving her home without her husband's permission for no necessity is considered an act of defiance (nushooz) that forfeits her right to maintenance. It is not permissible for a woman to travel without a mahram. The husband is advised to clarify this to his wife and to strive to bring her back with wisdom, using means of reconciliation, and seeking help from relatives. If these methods fail, he can refer the matter to the Sharia court. The wife must be warned that informing her husband that she has committed adultery is not permissible; either she is lying, or she is openly committing a sin, and neither is permissible.