The Securities and Exchange Commission has charged a Washington investment adviser with fraud in conjunction with an out-of-state stock manipulation case.

William C. Johnson was charged last week with making untrue statements to clients and realizing personal profits of $224,000 from the sale of the stock. The SEC has sought an injunction against him and others involved.

The case involves Gilman Services Inc., a drug wholesaler formerly located in Braintree, Mass. The SEC said two North Miami men, Michael A. Light and Michael F. Dermer, and three of their companies traded Gilman stock through 20 separate accounts at 10 broker dealers to create "a false appearance of active trading."

The price of Gilman shares rose from $4 to $25, then sank to $6 during a two-year period starting in March 1979. Gilman is now operating under Chapter XI bankruptcy laws.

The SEC alleges that Light and Dermer wrote nearly $500,000 in worthless checks to brokers to pay for the stock and make margin calls. They withdrew $1.5 million from their accounts, leaving brokers with unpaid debts of about $385,000. eparately, Johnson and Johnson Management & Co. was charged with sending "so-called research report recommendations" to 5,000 investors and broker dealers. Johnson, according to the complaint, predicted Gilman would capture 10 percent of the market thanks to a new product, Zeroid, which it said had been patented and approved by the Food and Drug Administration, when in reality the patent was only pending.

Johnson failed to disclose that he purchased 89,200 shares of Gilman for himself, his mother and several clients "on whose profits he was to receive a 20 percent fee," the SEC said. After the price run-up, Johnson sold the stock and pocketed a $244,000 profit.

Willis Riccio, SEC regional administrator in Boston, said Johnson was not involved in a conspiracy with the others but benefited from their actions. He did not exclude the possibility that Johnson might be asked to give up the profits.

Johnson Management is located at 1000 Wisconsin Avenue NW. A caller asking for Johnson was referred to Reliable Pharmaceuticals at the same address. Johnson, who is listed as president of that company, did not return calls.