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Gainesville police have arrested three men they say are responsible for the shooting after Richard Spencer's speech at the University of Florida on Thursday.

Tyler Tenbrink, 28, of Richmond; William Fears, 30, of Pasadena; and Colton Fears, 28, also of Pasadena, were each arrested on charges of attempted homicide and were being held Friday in the Alachua County, Fla., jail.

At least two of the men are linked to "extremist groups", police said, without specifying which two.

Detectives said Tenbrink "willfully and willingly fired a deadly weapon" with the "intent to kill", according to his arrest report.

Around 5:50 p.m., the men pulled up in a silver Jeep next to a small group of people sitting on a bus bench, according to Alachua County deputies.

Tenbrink fired a single shot toward someone in the group, police said.

I am amazed that immediately after being shot at, a victim had the forethought to get the vehicle's license number. Multiple local police units and the Florida Highway Patrol conducted a high-risk felony traffic stop on Interstate 75 near High Springs and Lake Butler, and the three Texas men were arrested.

The Fears brothers are each being held on $1 million bond.

The office said in a tweet that he had brought a gun onto the campus after being hired by a media organisation as security.

A video taken by a Tampa Bay Times reporter following Spencer's speech appears to show Tenbrink getting surrounded by protestors before he hopped over a fence.

Florida's governor had declared a state of emergency for the event.

As the man walked through the crowd, he was quickly surrounded by protesters and chanting.

The vehicle drove about 10 feet and stopped. There were a few scuffles on campus that left five people with minor injuries, the university said in a statement.

"We had complete unknown about the numbers of people who they may be coming to our area and what their intent would be", said Sheriff Darnell.

Spencer is the president of a group called the National Policy Institute, which asked to organize an event at the university, a public school.

"I would like to thank Gainesville for showing outsiders that our town is no place for hatred to exist", said Spokesperson for the Gainesville Police Department, Officer Ben Tobias.

Gainesville police will release more details in the future.