Merseyside Police Assistant Chief Constable Jon Roy said the two officers needed medical treatment for injuries to their backs after bottles were thrown at them as they went to help an assault victim in a crowd of supporters at the Pier Head on Friday night.
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"They were committing acts of disorder and then threw glasses and bottles at the police when they tried to intervene."
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Fifteen people were arrested for public order offences, affray and being drunk and disorderly and one man was arrested on suspicion of assault after another suffered serious head injuries, police said.
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"Specially trained officers in protective kit had to disperse them and we then had a number of really violent, absolutely unacceptable, incidents of violence and disorder throughout the city centre."
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Mr Roy said by the time police arrived at the Pier Head at about 4pm, around 500 people were already there and within 35 minutes the numbers had doubled and people were continuing to arrive.