Does a husband break his oath after swearing on the Qur'an that he would not speak to girls, and then it is discovered that he does so, and does divorce occur in this case?

If the husband swore by the Quran to stop speaking with girls, and then spoke with them, he has broken his oath and must offer an expiation for it. As for his informing the girls that he has divorced, if he was lying, the preponderant opinion is that his divorce does not take effect. He must repent from lying and from speaking with non-mahram women.