Last year AXA Private Equity and Permira competed fiercely in takeover battles of two European travel websites.
Unions have been critical of the treatment of employees at two of Permira's businesses: the AA and Birds Eye.
The AA got rid of 3, 000 staff - more than a quarter of its workforce - while under Permira's ownership.
In 2012 Rosso tried to buy Italian couture house Valentino, put up for sale by London private equity outfit Permira.
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Once a public company, NDS previously was taken private by the private equity shop Permira and by News Corp.
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But Mr Buffini takes the examples of New Look and Travelodge as businesses that have expanded and taken on extra staff since Permira invested in them.
In a memo prepared for tax authorities while the investigation was continuing, Vittorio Marzotto wrote that the sale to Permira was an "unhoped for and unexpected" outcome.
One reason, says Damon Buffini of Permira, is that whereas America has already unbundled most of its badly run conglomerates, Europe is only now starting to do so.
With their recently formed alliance AXA and Permira are hoping to merge Opodo with Go Voyages and eDreams to create a proper European rival to Orbitz and Expedia, two American firms which are the market leaders.
Permira Advisers and TPG Group.
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As is by now well known, the partners of private equity firms such as Blackstone, KKR, Permira, TPC, CVC, BC Partners among many others became wealthy beyond most people's wildest dreams - to the tune of tens of millions of pounds, hundreds of millions of pounds and in some cases billions of pounds.
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