The new school rector, a student's representative at the university court, will be voted on in February. Snowden, who is living in Russia after fleeing the United States following his disclosure of the National Security Agency's domestic snooping activities, is one of four candidates.
A statement from the on-campus group supporting his candidacy referred to "ending state intrusion into our private lives" in announcing his entry into the contest.
Snowden, a former NSA contractor, is not connected with Glasgow University, and the Scottish television channel STV did not indicate whether Snowden approved the nomination.
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