January 15, 1986

A little more than a year after the International Business Machines Corporation bought the Rolm Corporation, M. Kenneth Oshman, Rolm's president and the moving force behind its ascendancy in the telecomunications industry, said yesterday that he would resign. ''I've done my thing, and it's time to move on,'' the 45-year-old Mr. Oshman said in a telephone interview from Rolm's Santa Clara, Calif., headquarters. ''I'm not certain what I'm going to do next, but I'm certainly not going to sit around and watch TV.'' Mr. Oshman's departure, the first by a top-level Rolm executive since I.B.M.'s $1.25 billion acquisition late in 1984, immediately prompted speculation in the computer industry that I.B.M. was seeking stronger control over the free-wheeling telecommunications company.

Predicting ''a new economic resurgence for New York,'' Governor Cuomo today proposed a $41.4 billion state budget that would increase spending by 7 percent while also putting into effect the second year of a tax-cut plan. ''This is a budget that moves us forward in a balanced way,'' the Governor said. ''It is balanced arithmetically, it is balanced regionally, it is balanced socially and it is balanced programmatically.'' The budget, for the fiscal year that begins April 1, calls for more spending on the homeless and on victims of acquired immune deficiency syndrome, a 5 percent increase in state aid to local schools and the hiring of more prison guards and state troopers. Aid to Local Governments It would increase total state aid to local governments by 6.6 percent, with the administration saying that New York City would receive 5.5 percent more than last year. As expected, however, the Governor would provide no money to compensate municipalities for a possible Federal aid reduction, saying that to do so would encourage Washington to make the cutback.

The caption of a picture by United Press International on Thursday with an article about the trial of police officers in Miami misidentified one person in the courtroom. He was Gregory Denaro, a defense lawyer, not Armando Garcia, a defendant.

Prime Minister Margaret Thatcher, facing what is rapidly developing into her most severe political test since the Falkland War, rallied today to the defense of a key member of her Cabinet, who is accused of misleading the House of Commons. The Cabinet member, Leon Brittan, the Secretary for Trade and Industries, was already at the center of a furious controversy within the governing party over the future of a nearly bankrupt helicopter company when he stumbled into further trouble on Monday. He was forced to go before the House late Monday night to offer an explanation and apology for failing to acknowledge his awareness of a letter that had been the subject of three parliamentary questions in the afternoon. The letter had to do with the controversy over the Westland helicopter company, which led last week to the theatrical resignation of Defense Secretary Michael Heseltine, who walked out of the Cabinet room at 10 Downing Street, the Prime Minister's official residence.

The Economy New-car sales fell 8.3 percent in early January from year-earlier levels, despite renewed incentives, Detroit's car makers said. Light-truck sales dropped 19.2 percent. Analysts were disappointed, saying sales are still feeling the effects of the surge brought on by sales incentives in August and September. [ Page D1. ] Retail sales rose 1.9 percent in December, spurred by a rebound in auto demand then. [ D4. ] Americans took on $4.88 billion more in consumer debt than they paid off in November, the smallest increase in more than two years. [ D2. ] Automatic spending cuts will force widespread curtailments in most non-military Federal programs. They will also cut the military budget for the first time in 13 years. [ A1. ]