Police have released the names of two students who were killed in a mass shooting at Michigan State University on Monday night. 

The two victims are Brian Fraser, a sophomore at Michigan State originally from Grosse Pointe, Michigan, and Alexandria Verner, a junior from Clawson, the MSU Department of Police and Public Safety announced in a statement on Tuesday. 

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"Alex was and is incredibly loved by everyone," Clawson Public Schools Superintendent Billy Shellenbarger said in a statement. "She was a tremendous student, athlete, leader and exemplified kindness every day of her life."

Fraser and Verner were among three students who were fatally shot during the massacre, although authorities declined to publicly identify the third student at the request of that individual's family. 

"The Michigan State University Department of Police and Public Safety (MSU DPPS) is saddened to share information regarding the tragedy that occurred on campus Monday evening. We cannot begin to fathom the immeasurable amount of pain that our campus community is feeling," MSU police said in the statement. "We want to ensure our community that our department as well as our law enforcement partners will conduct a comprehensive and thorough investigation regarding this tragic incident."

Phi Delta Theta, a fraternity at Michigan State where Fraser was a chapter president, responded to the news of his death on Tuesday afternoon.

"Phi Delta Theta International Fraternity was devastated to learn that Brian Fraser, chapter president of the Michigan Beta Chapter of Phi Delta Theta at Michigan State University, tragically lost his life on the evening of February 13," the organization wrote on Twitter. The tweet included three photographs of Fraser, one of which pictured him standing with a group of peers on the grounds of the MSU fraternity house.

The fraternity praised Fraser's leadership and described him as "a great friend" in a lengthier statement.

"As the leader of his chapter, Brian was a great friend to his Phi Delt brothers, the Greek community at Michigan State, and those he interacted with on campus," the statement read. "Phi Delta Theta sends its deepest condolences to the Fraser family, the Michigan Beta Chapter, and all those who loved Brian as they mourn their loss."

Phi Delta Theta is coordinating with MSU "to connect the chapter with local campus services and opportunities to appropriately celebrate Brian's life."

In addition to those who died in Monday's shooting, five Michigan State students were shot and sustained critical injuries. All five were transported to Sparrow Hospital nearby for treatment in the aftermath of the massacre, officials confirmed earlier on Tuesday, saying that four of them required surgery and underwent those procedures immediately. 

Each of the five injured students remained hospitalized in critical condition on Tuesday afternoon, said Dr. Denny Martin, the interim president and chief marketing officer at Sparrow Hospital, in an update shared with CBS News. At the time, Martin said that one of the students was alert and interacting with members of their care team. None of the injured students has been publicly identified.

Law enforcement officials identified the gunman as Anthony Dwayne McRae, a 43-year-old man who, police said, did not have any clear affiliation to Michigan State or its community. Responding to a tip, authorities located McRae's body about three hours after the mass shooting took place, at around 11:30 p.m. on Monday night, according to MSU public safety. 

The suspect was found dead in the city of Lansing of a self-inflicted gunshot wound, police said. He was found with a note in his pocket that "indicated a threat" to two other schools in Ewing Township, New Jersey, officials confirmed, prompting both schools to close temporarily on Tuesday.