MEXICO CITY — Mexican officials said Friday that they had detained a leader of the criminal group that prosecutors believe killed 43 college students, then burned their bodies in a case that continues to roil the country more than three months after the young men disappeared.

The arrest of Felipe Rodríguez Salgado, who was being questioned late Friday, may add more details to the theory that the authorities have outlined.

Prosecutors say that the municipal police in the southern city of Iguala, in the state of Guerrero, had arrested the students and handed them over to the Guerreros Unidos organized-crime group on orders from the city’s mayor, José Luis Abarca.

Mr. Abarca and his wife, María de los Angeles Pineda Villa, are believed to be closely linked to Guerreros Unidos. The pair fled Iguala, then were arrested in Mexico City in November. The authorities formally charged Mr. Abarca with kidnapping in the students’ disappearance on Tuesday. At the same time, Ms. Pineda was charged with involvement in organized crime.