Blackstone Group LP has ended its pursuit of Dell Inc., less than a month after the private-equity firm said it would try to top a leveraged buyout by the computer maker's founder and a rival investment firm.

Blackstone had been putting together a bid for Dell to trump the $24.4 billion offer from founder and Chief Executive Michael Dell and private-equity firm Silver Lake Partners. Blackstone's offer would have kept part of the company in the hands of public shareholders.

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