Is it permissible for a wife to go out to study without the permission of her imprisoned husband, given that his family is aware of it?

A woman is not permitted to go out to study without her husband's permission, even if he is imprisoned and she cannot inform him, or if his family knows.

However, she is permitted to go out to study without his permission in two cases: 1. If the study is related to learning individual obligations (furood al-ayaan) such as prayer, fasting, and zakat, and she cannot learn them except by going out. 2. If she knows from her husband's usual behavior that he would permit her in such cases, and her going out does not lead to committing something forbidden, then customary permission takes the place of actual permission.