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The chief executive of British music charity Rhythmix has written an open letter to Simon Cowell appealing for the "X-Factor" boss to stop using the organization's name for one of the acts in this year's U.K. competition.

Four-piece girl group Rhythmix were put together by judges in the current U.K. series of "The X-Factor," having previously auditioned as individual contestants. "X-Factor" producers have lodged an application in Europe to trademark the group's name.

That decision, however, has brought the Cowell-owned TV show into direct dispute with a Brighton-based charity also called Rhythmix, which provides music training and opportunities to children living in the South East of England. Since opening in 1999, Rhythmix says that it has worked with over 40,000 people, "enabling their creative activity through music and developing their personal and social skills."

According to the charity's chief executive Mark Davyd, Simco Limited -- which is majority owned by Cowell -- applied to trademark the name Rhythmix on September 23, 2011 despite being "fully aware that Rhythmix was an existing trademarked name of a music charity that works with vulnerable young people."

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"By pursuing these trademarks Simco is forcing the Charity to take legal action to ensure it can continue to exist," Davyd goes on to say in an open letter published today via Facebook. Although Simon Cowell is not a judge on the current U.K. series of "The X-Factor," due to his commitments with the debut U.S. series, he remains the show's executive producer, while many of the most popular acts from each series receive recording contracts with his Syco label, in conjunction with Sony Music.

"We don't buy this media invention of you as Mr. Nasty," Davyd continues. "Your Wikipedia entry explains at length your involvement with children's charities, and we commend you for it. But equally we don't believe that you are unaware of the way your own company is acting. Or maybe your staff are trying to 'manage' it for you?"

The open letter closes by saying: "Every legal action the Charity has to take to protect itself from Simco is a project that won't happen. A project that could make a difference to a vulnerable young person. A large number of the public reading this will see it for exactly what it is; a ridiculously overblown storm in a tiny teacup. Simco are solely responsible for that situation and you can resolve it in a matter of seconds. For that reason, Simon, we are personally asking you to sort this problem out in the quickest and simplest way: Just change the name."

At press time, a representative of Simco Ltd could not be reached for comment. Speaking to the BBC, a spokesperson for "The X-Factor" said: "The charity in question have trademarked the name Rhythmix for educational purposes only, which is not in conflict with the band or the show."