Next year, if all goes as planned, the largest maker of personal computers in Asia will become the third largest in the world.

Lenovo Group Limited of China is buying the personal computer business of the American company I.B.M. International Business Machines brought millions of people their first P.C.'s. Now it is getting out of the business of selling them. Aggressive competition in the industry has cut the profit in sales.

The deal is worth one thousand seven hundred fifty million dollars. This includes five hundred million dollars in debt that Lenovo will take over from I.B.M. Lenovo will be third in worldwide sales behind the American companies Dell and Hewlett-Packard.

Ten thousand I.B.M. employees will go to work for Lenovo. The American company already has thousands of employees in China. I.B.M. will hold a nineteen percent share in Lenovo. And I.B.M. will continue to offer services, the most profitable part of its personal computer business.

I.B.M. helped create the market for personal computers in nineteen eighty-one with a machine that became very popular. The computer used an operating system made by a small company, Microsoft. Another small company provided the microprocessor, the brains of a computer. That was Intel. Intel and Microsoft grew highly profitable.

But soon, less costly computers appeared. I.B.M. saw its market share shrink. In the end, it stopped making its personal computers itself.

The Gartner research group estimates that I.B.M. had a five percent share of the world P.C. market this year. Lenovo had two percent. But it controls one-fourth of the Chinese market, the largest in Asia. Lenovo was formerly known as Legend Computer. Members of the Chinese Academy of Sciences began the company in nineteen eighty-four.

Chinese companies are moving to expand their international business holdings. This purchase is one of the biggest yet. Lenovo will be able to use the I.B.M. name for five years.

Lenovo will have the headquarters of its personal computer business in New York, with operations in Beijing and Raleigh, North Carolina. Stephen Ward will be the chief executive officer and Yang Yuanqing will be the chairman. Officials expect the deal to be made final by the middle of next year.