Is it permissible for a wife whose rights have been violated for a long period of time by her husband to seperate from him and go live somewhere else?

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It is not permissible for her to do that, but she can raise her case to the legal ruler (the mujtahid), and he will give him the choice between living with her in a kind manner, spending on her and divorcing her. If he refused to do so, the legal ruler will divorce her.