Is it permissible for a husband to divorce his wife who leaves their home without his knowledge, lies to him, and neglects prayer, after disputes concerning her studies and work?

A wife's departure from her home without her husband's permission is considered an act of defiance (nushooz). The husband should remind her of Allah and warn her of His punishment. If she does not respond, he should forsake her in bed. If that does not correct her, he may strike her a non-injurious blow, as stated in the Almighty's قول: "As for those [wives] from whom you fear defiance, admonish them, forsake them in beds, and strike them. But if they obey you, seek no means against them." [An-Nisa: 34] Furthermore, a wife's father assisting her in disobeying her husband is considered instigation and corruption. The wife must repent from disobeying her husband and neglecting prayer, and her father must fear Allah. The husband should be patient and deliberate before divorcing, and attempt reconciliation by involving people of sound judgment. If she mends her ways, then well and good; otherwise, he may divorce her. A defiant wife has no right to maintenance, but the husband is obligated to provide for his daughter.