What is the ruling on a wife's repeated requests for divorce due to marital problems, accompanied by her raising her voice at her husband and his hitting her, and is the husband permitted to grant her request?

A wife is not permitted to seek divorce without a legitimate reason. If she seeks it for the slightest disagreement, then she is disobedient (nashiz), and the treatment for disobedience has clear, established steps. Striking is not the first solution, and it has its own regulations. The husband is not obligated to divorce her, but if the marital relationship deteriorates and reconciliation proves futile, then divorce is preferable.