Wife beating is entirely permissible, encouraged even, in accordance with Islamic law.

“Men are the maintainers of women because Allah has made some of them to excel others and because they spend out of their property; the good women are therefore obedient, guarding the unseen as Allah has guarded; and (as to) those on whose part you fear desertion, admonish them, and leave them alone in the sleeping-places and beat them (Quran 4:34)

“And take in your hand a green branch and beat her with it, and do not break your oath (Quran 38:44) –

“A woman came to Muhammad and begged him to stop her husband from beating her. Her skin was bruised so badly that it is described as being “greener” than the green veil she was wearing. Muhammad did not admonish her husband, but instead ordered her to return to him and submit to his sexual desires. Sahih Bukhari (72:715)

“Muhammad struck his favorite wife, Aisha, in the chest one evening when she left the house without his permission. Aisha narrates, “He struck me on the chest which caused me pain.” Sahih Muslim (4:2127)