The Carlyle Group is an American-based global asset management firm, specializing in private equity, based in Washington, D.C.. The Carlyle Group operates in four business areas: private equity, real assets, market strategies and fund of funds, through its AlpInvest subsidiary.   Carlyle's private equity business has been one of the largest investors in leveraged buyout transactions over the last decade, while its real estate business has actively acquired commercial real estate. Since its inception, Carlyle has completed investments in such notable companies as Booz Allen Hamilton, Dex Media, Dunkin' Brands, Freescale Semiconductor, Getty Images, HCR Manor Care, Hertz, Kinder Morgan, Nielsen and United Defense.   The Carlyle Group LP, one of the country's largest private-equity firms, reported a slight rise in quarterly profits on Thursday, mostly because of a 7 percent gain in the value of its investments. The Washington-based private equity fund reported economic net income of $394 million in the three months ending March 31, up from $392 million the year before. After taxes were taken out, Carlyle's net income worked out to $1.02 per share. That beat analysts' estimates of 94 cents, according to FactSet. Carlyle became a public company last May, so it didn't provide prior year per-share numbers.