Polish authorities have opened an investigation into the attack, in which the four men are accused of badly beating up the woman's boyfriend before attacking her. They are also accused of raping a Peruvian transgender woman on the same night.
Patryk Jaki, Poland's deputy justice minister, said the four should face a severe punishment "as an example", however it is not yet clear if Italy will allow the extradition.
The suspected 'leader' of the gang, a 20-year-old, was arrested on a train on Sunday, the last of the four to be arrested and the only adult among the suspects.
Two other members of the gang, brothers aged 15 and 17, handed themselves into police in connection with the rapes on Saturday - reportedly after their father recognized the boys in CCTV images and told them to report themselves. A third suspect aged 16 was detained shortly afterwards.
On Tuesday, a judge in Bologna upheld the arrest of the 20-year-old and ruled that the three minors be held on remand in jail, and that they should be prevented from communication with each other.
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