The Federal Reserve has moved into the Financial General Bankshares case, launching an investigation of plans by a Grand Cayman Island company and four Arab investors to offer to buy the Washington bank holding company.

The investigation could delay or block plans of International Credit and Investment Company (Overseas) Ltd. of Grand Cayman and the Arabs to make a tender offer of $15 a share for all the outstanding stock of Financial General.

The tender offer was required by the Securities and Exchange Commission as part of the settlement of securities law violation charges against ICIC, the Arabs, Bert Lance and others who bought about 20 percent of the bank's stock.

The SEC said the Lance group broke the law by not publicly reporting the stock purchases and by paying some sellers more than the market price for their stock without giving other shareholders the opportunity to sell at the same price.

As a remedy, the SEC a week ago required the buyers to offer the highest price paid - $15 per share - for all the outstanding shares in a public tender offer.

Federal Reserve officials, however, say that any company that seeks control of a bank has to undergo rigorous scrutiny and be qualified by the agency as a bank holding company.

An individual can buy a bank without federal approval, but a company that buys a bank is subject to extensive federal regulation, a Federal Reserve attorney pointed out. Even if the four Arab investors make the tender offer without ICIC, they could be determined to be a partnership and would face the same Federal Reserve review.

Extensive disclosures of a company's ownership and operations are required before a concern can be qualified as a bank holding company, the Federal Reserve sources said.

ICIC is a little-known international holding company that until now has made few disclosures about its operations. It was organized on Grand Cayman Island, a part of the Bahamas, where taxes are very low and bank secrecy laws are at least as protective as those of Switzerland.

Reports to the SEC say ICIC owns a majority interest in Bank of Credit and Commerce International, a Luxembourg organized, London-based bank run by Agha Hasan Abedi, a Pakistani banker. Abedi also heads ICIC, the SEC documents say.

Originally, BCCI was charged in the SEC complaint. Only when the case was settled was it revealed that ICIC was actually the firm involved in the purchases of Financial General stock.

BCCI's 1976 annual report makes no mention of its relationship to ICIC, and does not even name what is apparently its parent corporation.

Such secrecy will be impossible to maintain if ICIC gets involved in the tender offer for Financial General, Federal Reserve sources say. ICIC would be required to make public its ownership, which reportedly includes the heads of several Middle Eastern royal families, who have invested in the Grand Cayman company because of its secrecy.

Robert Altman, the attorney for Lance, Abedi, ICIC and the Arabs, said this week he plans to proceed with the tender offer as quickly as possible. The SEC settlement set a one-year deadline for the tender.