The self-immolation in October 2012 of 26-year-old Sangye Gyatso from Duohe village was "masterminded" by members of the Tibetan Youth Congress, police said.
Police said Gyatso was held in 2007 for repeated acts of theft. He had been without a formal job for a long time.
Khyi Gyatso, a 33-year-old monk at the local Duohe monastery, introduced Sangye Gyatso to ideas about "Tibetan independence", said police.
Khyi told Sangye to "contribute to the cause of Tibetans and improve his status and that of his family" by the "heroic deed" of self-immolation, Xinhua said.
On Oct 6, 2012, Sangye Gyatso set himself on fire, and Tashi Gyatso and Gonpo Je, who were there, took photos of the self-immolation.
Gansu police have arrested seven suspects, including Kalzang Gyatso, Gonpo Je and Tashi Gyatso.
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Chinese police have requested their counterparts in "relevant" countries help investigate the case.
Police said organising, masterminding and inciting self-immolations was a serious crime, intentionally depriving others of their lives.