NEW YORK (CBSNewYork/AP)Janet Jackson joins her brother Michael and the Jackson 5 as members of the Rock and Roll Hall of Fame, earning induction on Thursday along with Stevie Nicks and the top fan vote-getter, Def Leppard.

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Radiohead, the Cure, Roxy Music and the Zombies will also be ushered in next spring at the 34th induction ceremony. It will be held March 29 at Barclays Center in Brooklyn.

Jackson’s induction comes after her third time as nominee and many saw it as overdue, given her prowess as a hitmaker with “All For You,” ”That’s the Way Love Goes,” ”Nasty,” ”Together Again” and “What Have You Done For Me Lately.”

Janet Jackson performs onstage during the 2009 MTV Video Music Awards at Radio City Music Hall in 2009. (Photo by Christopher Polk/Getty Images)

Her career has suffered from the fallout after the infamous 2004 Super Bowl appearance where her bare breast was briefly exposed. Jackson became eligible for the rock hall in 2007 and wasn’t nominated until 2016.

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The Roots’ Questlove, in a social media post earlier this year, said her exclusion had been “highly criminal.” He cited the influence of her 1986 album “Control,” which he said set off the New Jack Swing trend.

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I’m using my platform for #JanetJacksonAppreciation day for a slightly different reason: as a voting member of the @RockHall its criminal that @JanetJackson has NOT been inducted yet. 32 years ago today #Control dropped AND CHANGED EVERYTHING: including her brother AND the mentor of her producers jimmy & terry. Whether we credit it or not: Control was the first #NewJackSwing album. Yeah it was breakbeat free, but the young brash attitude made it a first. This was NOONEs kid sister. Prince famously drove to @flytetymejam’s house and threw the record at his door zero o’clock in the morning (hey, if you ain’t got no haters you ain’t poppin) not to take away from her peers in the RRHOF that made marks in the 80s. But half of them can NOT claim they changed music (this is just one album mind you) I know this tag is for other reasons but of all the double standard injustices, her not being inducted is HIGHLY criminal.

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“This was no one’s kid sister,” he wrote.

Jackson said on Thursday: “Thank you Rock and Roll Hall of Fame. I am truly honored and I am happy to be in there with my brothers.”

It will be Nicks’ second induction into the rock hall, since she’s already there as a member of Fleetwood Mac. She launched a solo career in 1981 with her duet with the late Tom Petty, “Stop Draggin’ My Heart Around.” Other hits followed, including “Edge of Seventeen,” ”Stand Back” and “I Will Run to You.”

Def Leppard earned more than half a million votes from fans, which are incorporated into more than 1,000 ballots from artists, historians, industry professionals and past winners in deciding who gets honored. The British hard rock band with a pop sheen were huge sellers in the 1980s on the back of songs like “Photograph” and “Pour Some Sugar on Me.”

Def Leppard singer Joe Elliott (credit: Kevin Winter/Getty Images)

Frontman Joe Elliott said he was initially ambivalent toward the honor until Jon Bon Jovi suggested it would change his life.

“When I look at the list of who’s in, it’s just obvious you’d want to be in that club, isn’t it?” he told Billboard earlier this year. “When you think that every band that means anything in the world, starting from the Beatles and the Stones and any artist that influenced them — your Chuck Berrys, your Little Richards, etc., etc. — then of course you want to be in. Why wouldn’t you?”

Def Leppard, Nicks and Roxy Music were voted in during their first years as nominees. Other 2019 nominees who didn’t make the cut included LL Cool J, Devo, Rage Against the Machine, MC5, John Prine, Todd Rundgren and Kraftwerk.

There’s some question about whether Radiohead will shrug its collective shoulder as an inductees. The English band seemed like generic grunge rockers on their initial hit “Creep,” but with the album “OK Computer” and beyond have become consistent sonic pioneers. Among its rock hall class, Radiohead has the most impact on the current music scene.

Thom Yorke and Jonny Greenwood of Radiohead perform live on stage at Sydney Entertainment Centre in 2012. (Photo by Mark Metcalfe/Getty Images)

In an interview with Rolling Stone earlier this year, Radiohead’s Jonny Greenwood said “I don’t care” when asked about the rock hall. Bandmate Ed O’Brien said, “culturally, I don’t understand it. I think it might be a quintessentially American thing.”

The Cure and frontman Robert Smith resist their initial label as goth rockers, champions of fans who like black makeup, black clothes and darkly romantic songs. They have a durable catalog of hits, including “Friday I’m in Love,” ”Boys Don’t Cry,” ”Pictures of You” and “Let’s Go to Bed.”

(L-R) Porl Thompson, Jason Cooper, Robert Smith and Simon Gallup of The Cure pose backstage at the Teenage Cancer Trust organised by the Who’s Roger Daltrey in London. (Photo by Jo Hale/Getty Images)

Roxy Music came out of the 1970s progressive rock scene and had hits with “Love is the Drug” and “More Than This.” Dapper member Bryan Ferry had a successful solo career and Brian Eno has been an influential producer.

The heyday of British rockers the Zombies’ career was the 1960s, with big sellers “She’s Not There” and “Time of the Season.”

The hall will announce ticket sales for March’s ceremony next month. HBO and SiriusXM will carry the event.

(© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)