Does divorce occur by saying "you have received a divorce" with repetition, or by uttering the word "divorce" aloud for contemplation, or by gesturing to divorce with the phrase "what is between me and her is a word," or by uttering the explicit لفظ of divorce without intent, or by imitating a friend's oath of divorce?

Divorce occurs through an explicit pronouncement or an implicit one coupled with the intention of the responsible, consenting husband. The obsessive thoughts mentioned in the question do not constitute a divorce. Regarding swearing by divorce, the majority of scholars hold that divorce takes effect upon breaking the oath, whether the intention was divorce itself or merely emphasis, and this is the prevalent ruling. However, Sheikh al-Islam Ibn Taymiyyah is of the view that the ruling on swearing by divorce, when the intention is not to make the divorce conditional, is the same as swearing by Allah. If the oath is broken, the one who swore it must pay an expiation for an oath, and no divorce occurs. Furthermore, imitating a divorce pronouncement does not religiously constitute a divorce. However, imitating others mockingly to make people laugh is forbidden.