Does the divorce take effect with the words "by divorce it is lawful" (علي الطلاق حلال) when there was no intention of divorce, bearing in mind that the wife was menstruating at the time the utterance was made?

Your oath of divorce regarding the permissibility of the aforementioned matters has two scenarios:

1. If you believed them to be permissible at the time of the oath: The preponderant opinion is that divorce is not incumbent if the opposite becomes clear, even though some scholars hold that it is incumbent.

2. If you doubted their permissibility or believed them to be impermissible at the time of the oath: The preponderant opinion among the majority of scholars is that divorce occurs, even if the one swearing only intended an oath. Shaykh al-Islam Ibn Taymiyyah disagreed with this, holding that divorce does not occur if only an oath was intended.

The wife being in her menstrual cycle at the time of the oath does not affect the possibility of divorce occurring.