Is it permissible for a woman or a girl to lie on her back?

Lying down is permissible in principle, and nothing concerning it is disliked except with a legal proof. Narrations have been reported from the Salaf disliking a woman lying on her back. Umar ibn Abd al-Aziz disliked it for his daughters lest Satan become covetous, and Ibn Sirin and Imam Ahmad disliked it. The apparent reason for this dislike is the fear of fitnah (temptation/strife) and the exposure of awrah (private parts). If fitnah is secured, such as when the woman is alone or with her husband, then there is no dislike.