A class-action lawsuit filed Wednesday alleges that students denied admission to several prominent universities in recent years were deprived of a fair review because the schools failed to maintain adequate safeguards to prevent fraud that came to light this week in a cheating and bribery scandal.

The complaint, filed in federal court in Northern California, names several college and university students as plaintiffs acting on behalf of themselves and others in similar situations who applied to competitive schools. It is part of what could become a wave of litigation sparked by a federal investigation into a scheme to help children of wealthy parents secure entry to prestigious schools through cheating on admissions tests and bribery of athletic coaches. Fifty people, including numerous parents, were charged Tuesday in the scheme.

The students allege in their suit that the universities that were duped through the scheme were negligent in failing to take adequate steps to guarantee “the sanctity of the college admissions process.” Kalea Woods, now a Stanford University student, applied in 2017 to the University of Southern California, according to the suit. The suit said Woods was unaware when she applied that admission to those schools was “an unfair, rigged process” in which parents could “buy” slots for their children.

Other plaintiffs applied to the University of Texas, UCLA and other schools that were drawn into the scandal.

One plaintiff originally named in the case, Stanford student Erica Olsen, pulled out of the suit Thursday as the complaint was amended.

The plaintiffs are seeking a refund of their application fees and other damages.

Among defendants in the suit are William “Rick” Singer — a California man authorities say was the mastermind of the conspiracy — as well as Stanford, University of Southern California, Yale, University of California at Los Angeles, University of San Diego, University of Texas at Austin and Wake Forest and Georgetown universities.

Singer pleaded guilty Tuesday to conspiracy charges for racketeering and other crimes in federal court in Boston.

Federal investigators have not accused the universities of wrongdoing. But several athletic coaches formerly employed by the schools were charged with taking bribes in exchange for designating applicants as athletic recruits, even though they were not athletically qualified.

Asked about the lawsuit, UT-Austin spokesman J.B. Bird said Thursday in a statement: “Like many students and families across the country, we are also outraged that parents, outside actors and university employees may have committed fraud surrounding admissions at universities. The University of Texas has a thorough, holistic admissions process. The actions alleged by federal prosecutors against one UT employee were not in line with that policy and may have been criminal. They do not reflect our admissions process.”

Stanford said: “We believe the lawsuit filed by the students against Stanford is without merit. We take the issues raised through the events of this week very seriously. While we continue to closely examine our policies and processes to see if improvements should be made, we stand behind the integrity of our admissions process.”

U-San Diego said the suit is under review. USC said it has heard about the lawsuit but has not been served.

Georgetown said: “While we do not comment on pending litigation, Georgetown University takes the integrity of our admissions process seriously and is committed to a fair, holistic process whereby each application is carefully reviewed. We review all applicants without consideration of a family’s financial consideration or ability to pay.”

UCLA said it is “aware of the lawsuit and does not comment on pending litigation.”

Other schools named in the suit did not immediately respond to a request for comment.

This story has been updated.