A horrific video of the killings was posted on the YouTube video-sharing website.
One of those arrested was a traditional ruler in the Aluu community of Port Harcourt, police said, urging students from the University of Port Harcourt (Uniport) not to seek revenge.
The students had been accused of stealing laptops and mobile phones.
The video shows four men stripped naked, with tyres around their necks, being beaten by a mob with wooden sticks, before being set on fire.
One of their classmates, Paul Irabor, told the BBC that the four had left the university campus in Nigeria’s oil capital to collect some money they were owed, when they were mistaken for thieves.
Rivers state police spokesman Ben Ugwuegbulam confirmed the incident to the BBC.
“The Rivers state police command is strongly opposed to such barbaric conduct, and has commenced diligent investigation into the matter,” he said.
He added that the video was forming part of the investigation.
The BBC’s Bashir Sa’ad Abdullahi says that Nigerians, disillusioned with their police force, sometimes take justice into their own hands and lynch suspected robbers but the brutality – and the fact this incident was filmed and published on the internet – has shocked the country.
Peace FM Online
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