COLUMBIA — South Carolina agrees that major violations took place in its football program and will eliminate six football scholarships over the next three years as part of self-imposed penalties.

The school’s response Wednesday came three months after the NCAA accused the Game­cocks of receiving $55,000 in improper benefits for players staying at a Columbia hotel at a reduced rate and for its involvement with a Delaware-based mentoring group whose president and treasurer – South Carolina graduates – provided extra benefits.

The school said it would pay a fine of $18,500 for four football players who played in 2009 despite being ineligible because of these violations. It will also reduce the number of official visits for its football and track and field teams.

The university has disassociated itself from three boosters, including Student Ath­lete Mentoring Foundation president Steve Gor­don and treasurer Kevin Lahn.

Former head of compliance Jennifer Stiles was demoted for her office’s role in signing off on the hotel arrangements.

The school also offered a three-year period of probation.

“We continue to work in full cooperation with the NCAA on this very serious matter,” Pres­ident Harris Pastides said. “As an institution, we established self-imposed penalties and implemented corrective actions.”

The NCAA said in September that 10 football players and two members of the women’s track team stayed at a Columbia hotel for a reduced rate. The NCAA said the school commited a second major violation when athletes or prospects received $8,000 in benefits from Gordon and Lahn.

The NCAA will consider the self-imposed penalties at a hearing in February.