Three men were attacked in separate incidents in Bolton.
A 41-year-old white man was walking along Davenport Street and passed a group of black men in their late teens or early 20s at about 9.45pm on Monday January 11.
He walked on to Beta Street and noticed that three men from the group had followed him.
They started punching the victim in the head and accused him of being a racist.
He tried to walk away but the offenders continued to punch and kick him.
They demanded that he empty his pockets, stole his mobile phone and cigarettes and walked off.
The victim was taken to hospital with cuts and bruising and is awaiting test results to discover whether he has a fractured eye socket.
At about 10pm the same night, a CCTV operator noticed three black men punching and kicking a man lying on the ground in Duke Street North, School Hill.
Officers attended and found a 29-year-old man with minor facial injuries.
At 10.30pm, a 44-year-old man was walking along Topping Street when three or four men came up behind him and dragged him to the ground.
They punched and kicked the victim in his face and back, searched him and stole the rucksack from his back and all of its contents.
The victim was taken to hospital and treated for cuts and swelling to his face.
The offenders in this attack have been were described as Asian in their early 20s.
Detective Inspector Andy Cunliffe, from Bolton CID, said: "All of these attacks were entirely unprovoked. Two of them were robberies, in the first of which the offenders used the flimsy veil of a vigilante attack for racism.
"We are doing everything we can to ensure those responsible for all of these disgusting attacks are caught, including drafting officers from Greater Manchester Police's Tactical Aid Unit into the area.
"Colleagues from the Neighbourhood Policing Team will be out and about speaking to local residents whilst officers from the Bolton Robbery Unit will be following up on a number of leads."
Anyone with information is asked to call Bolton Robbery Unit on 0161 856 5609 or the independent charity Crimestoppers, anonymously, on 0800 555 111.
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