A Long Beach teenager pleaded guilty Friday to murdering a young woman on a footbridge in Rockville Centre and will serve 18 years to life in prison under terms of a plea deal.

Maxwell Sherman, 19, admitted to Judge Meryl Berkowitz in Nassau County Court that he killed Lauren Daverin-Gresham, 18, of Lynbrook the night of Aug. 22, 2013.

Police said the victim, who had never met her attacker before, was sexually abused, beaten and strangled.

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The victim's mother, Kathleen Daverin of Lynbrook, hugged Assistant District Attorney Everett Witherell outside court and thanked the prosecutors and police who worked on the case.

"I'm just glad justice was finally served for my little girl," Daverin told reporters on the steps of the Mineola courthouse.

Defense attorney William Petrillo of Garden City said a first-degree sexual abuse charge was dismissed as part of the deal. Sherman, who will be eligible for parole in 16 years, would have had to register as a sex offender on his release if convicted of the sex charge.

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Petrillo said outside court that Sherman's "state of mind from the beginning has been remorse, genuine remorse."

"His true desire from the beginning . . . [was] to spare both his family and the victim's family a long, drawn-out trial, and he has made a decision to accept responsibility," the attorney said.

The woman's bloodied body was found about 10 p.m. on a footbridge spanning eastbound Merrick Road in Rockville Centre, an area residents said was a popular late-night place for teenagers to gather and drink.

Sherman's family, who live in Illinois, have a second home in Long Beach. Prosecutors have never publicly offered a motive in the killing of Daverin-Gresham, who was married.

Sherman would have faced a maximum of 25 years to life in prison if convicted of the top count of second-degree murder. A conviction for sexual abuse could have added 7 years.

"With this top-count conviction, the defendant has admitted his guilt in the murder of 18-year-old Lauren Daverin and her grieving family is spared from having to relive this brutal crime through a trial," Nassau Acting District Attorney Madeline Singas said in a statement.

Sentencing is set for June 11.