(CNN) A group of students and parents have filed a federal lawsuit seeking class-action status against the University of Southern California, UCLA and other colleges named in this week's sprawling admissions scandal, saying their admissions process was "warped and rigged by fraud."

Prosecutors revealed Tuesday that 50 people, including 33 parents and a number of college coaches, face charges in carrying out a scheme in which wealthy people used their money to game the admissions system at some of the nation's elite universities.

As a result, the plaintiffs allege in part negligence, unfair competition and violations of consumer law, according to an amended lawsuit filed Thursday in US District Court for the Northern District of California.

The lawsuit names Stanford University, USC, UCLA, the University of San Diego, the University of Texas at Austin and Wake Forest, Yale and Georgetown universities as defendants. The schools were cited in the stunning nationwide conspiracy that federal prosecutors unveiled Tuesday. CNN is reaching out to the universities named for comment on the lawsuit.

The students and parents in the lawsuit said they spent money to apply to schools named in the college admissions scandal, and attorneys say they wouldn't have applied had they known about the alleged scheme.

"Had Plaintiffs known that the system was warped and rigged by fraud, they would not have spent the money to apply to the school," the lawsuit says. "They also did not receive what they paid for -- a fair admissions consideration process."

The lawsuit asks for a variety of relief, including compensatory and punitive damages, restitution and other relief deemed proper by court.

"The students who filed the complaint didn't receive what they paid for -- to participate in an application process free of fraud," said David Cialkowski, an attorney for the students. "It's a straightforward claim and a simple remedy. The students want their money back. They request that anyone who paid an application fee to any of the eight named universities but was denied admission gets their application fee returned."

Prosecutors say the schools are victims

On Tuesday, William Rick Singer , the man at the center of the scheme, pleaded guilty to racketeering, money laundering conspiracy, conspiracy to defraud the United States and obstruction of justice in federal court in Boston. Singer and his nonprofit, the Key Worldwide Foundation, and his college counseling business, the Key, also are defendants in the students' lawsuit.

Prosecutors have said the universities are victims in the criminal case, and the schools have made similar assertions. In addition, US Attorney Andrew Lelling said the students accepted fraudulently took the place of a deserving student.

"For every student admitted through fraud, an honest genuinely talented student was rejected," he said.

In particular, court documents detail how Stanford sailing coach John Vandemoer agreed to designate a prospective student as a recruited sailor, facilitating the student's admission to Stanford, in exchange for a bribe. Singer sent $110,000 to the Stanford sailing program for one student and $160,000 to the program for another student, documents state.

Neither student ended up attending Stanford, according to the documents.

Vandemoer pleaded guilty Tuesday to racketeering conspiracy. Stanford said it has been cooperating with the Justice Department in the case and has fired the coach.

"Let us be clear: The conduct reported in this case is absolutely contrary to Stanford's values, and to the norms this university has lived by for decades," President Marc Tessier-Lavigne and Provost Persis Drell said in a statement Tuesday. "Today's news is a shock exactly because it so clearly violates our institutional expectations for ethical conduct.''

But Stanford said the students' lawsuit is without merit.

"We take the issues raised through the events of this week very seriously," E.J. Miranda, the school's senior director of media relations, said in a statement. "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."

This story has been updated after a student and her mother named in the court documents said they do not want to be part of the lawsuit.