FLORENCE, Italy (AP) — DNA analysis of a condom and cigarette butt led Italian prosecutors to arrest a Senegalese immigrant in the death of an American woman who suffered two fractures to her skull before being strangled in her Florence apartment, they said Thursday.

The naked body of Ashley Olsen, 35, of Summer Haven, Florida, was discovered Saturday morning by her boyfriend.

Florence chief prosecutor Giuseppe Creazzo told a news conference that investigators had detained the prime suspect in her death, Tidiane Cheik Diaw, a 25-year-old Senegalese immigrant, based on witness testimony and DNA analysis, and also because he had Olsen's cell phone.

He said investigators had no motive.

Citing witness testimony and street cameras, Creazzo said Olsen and Diaw met for the first time at the Montecarla disco in Florence early Friday morning and went together to Olsen's apartment in the Tuscan city's historic center.

He said they had consensual sex. Both had drunk alcohol and possibly taken drugs over the course of the night.

He said the autopsy determined that Olsen had also suffered two fractures to her skull before she was strangled.

Police detained Diaw after DNA analysis came back from a used condom and cigarette butt found in Olsen's bathroom, as well as DNA samples taken from under her fingernails.

Diaw was also tied to the crime because he had taken Olsen's cell phone, put his own SIM card in it and used it, Creazzo said.

Creazzo said Diaw had arrived in Italy illegally a few months ago to join his brothers who had been there for some time. He told investigators he was working odd jobs handing out flyers for local nightspots.

Diaw is accused of aggravated homicide, given the brutality of the death and that Olsen was in a compromised state, Creazzo said. He remains in detention.

Olsen moved to Florence a few years ago and was active in the expatriate arts scene. Her father is a professor at a local design institute.