SARAJEVO, Bosnia and Herzegovina — The bloody coup attempt in Turkey last week, which cost more than 200 lives, brought the world’s attention to the group that President Recep Tayyip Erdogan declared responsible: the Islamic community led by Fethullah Gulen, a Turkish cleric who has lived in self-imposed exile in Pennsylvania since the late 1990s.

Mr. Gulen strongly denies the charges. Some in the West seem to think that this is yet another of the many bizarre conspiracy theories peddled by Mr. Erdogan. But this is not merely propaganda. There are good reasons to believe the accusation is correct.

The Gulen community is built around one man: Fethullah Gulen. His followers see him not merely as a learned cleric, as they publicly claim, but the “awaited one,” as I have been told in private. He is the Mahdi, the Islamic version of the Messiah, who will save the Muslim world, and ultimately the world itself. Many of his followers also believe that Mr. Gulen sees the Prophet Muhammad in his dreams and receives orders from him.

Besides Mr. Gulen’s unquestionable authority, another key feature of the movement is its cultish hierarchy. The Gulen movement is structured like a pyramid: Top-level imams give orders to second-level imams, who give orders to third-level imams, and it goes on like that to the grass roots.