Nafi' narrates from Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) that a man performed li'an against his wife and disowned his child, so the Messenger of Allah (peace and blessings be upon him) separated the two of them and gave the child to the woman.
Note: In the hadith of Sahl there is the possibility of three divorces; because he knew his own truthfulness and was certain of his wife's lying and of her boldness in denying it, he pronounced three divorces out of not knowing, since li'an is in itself a separation. So he was like one who divorces a woman who has already been separated from him without his divorce, and like stipulating a warranty in a sale and a guarantee in a salaf (advance-payment) transaction, although it is binding whether one stipulates it or not. Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) narrates from the Prophet (peace and blessings be upon him) that he (peace and blessings be upon him) separated the two who performed li'an; so the Prophet's (peace and blessings be upon him) separating them is something other than the husband's separating; it is a separation that he (peace and blessings be upon him) decreed as a ruling.
Ikrimah narrates from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both), in the story of Hilal bin Umayyah, that the Messenger of Allah (peace and blessings be upon him) ruled that the mother and the child are not to be reproached, and whoever accuses them is to be given the prescribed punishment (hadd), and that this woman is entitled to neither food nor housing, because they were separated without divorce and without death.
This narration confirms what Imam al-Shafi'i (may Allah have mercy on him) said.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب اللعان / 15328