Blackstone Group LP raised $4.13 billion yesterday in the biggest US initial public offering (IPO) in five years selling a 12.3% stake that values the company at $33.5 billion.It sold partnership units at $31 each - the top of the range used to market the securities. The New York-based firm will use the money to expand its buyout and asset management units, and pay founders Stephen Schwarzman and Peter G. Peterson a combined $2.33 billion. The expected debut today of Blackstone on the New York Stock Exchange under the symbol "BX" will mark a watershed event for the booming private equity industry.The IPO valued Blackstone at about 12.6 times 2006 profit of $2.66 billion. Blackstone, the owner of companies with about 375,000 employees and $83 billion in annual sales, may wind up raising as much as $7.75 billion. Underwriters have the option to increase the sale of 133.3 million units by 20%, and China's soon-to-be-formed State Investment Co. will buy $3 billion of non-voting stock.