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LONDON — Traders with such nicknames as the ‘‘Three Musketeers’’ and the ‘‘A-Team’’ plotted through Internet chat rooms to manipulate currency markets for years, profiting at the expense of clients and then congratulating themselves for their brilliance in profanity-laced banter, regulators said Wednesday, as they fined five banks $3.4 billion.

Citibank, JPMorgan Chase, Royal Bank of Scotland, HSBC Bank, and UBS agreed to the settlements with the US Commodity Futures Trading Commission, UK Financial Conduct Authority, and Swiss Financial Market Supervisory Authority. The British regulator said Barclays remains under investigation.

‘‘Today’s record fines mark the gravity of the failings we found, and firms need to take responsibility for putting it right,’’ said Martin Wheatley, chief executive of the FCA. ‘‘They must make sure their traders do not game the system to boost profits.’’

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Meanwhile, a US Treasury Department agency revealed that it was fining three of the biggest US banks — JPMorgan Chase, Bank of America, and Citigroup — a total $950 million after finding that they failed to prevent misconduct in their foreign exchange trading operations.

About $5.3 trillion changes hands every day on the global foreign exchange market, with 40 percent of trades occurring in London. The market is loosely regulated and dominated by a few elite banks.

Manipulation of the exchange rates has ‘‘a profound effect on the economy,’’ said Aitan Goelman, enforcement director for the Commodity Futures Trading Commission.

That’s because a host of financial investments bought and sold by major investors such as pension funds are based on benchmark rates for pairs of currencies that are fixed daily by the banks.

With so much money flowing through the currency markets, a rigged procedure of fixing exchange rates can ripple through the financial system, the regulators say, and it also shakes people’s confidence in the fairness and integrity of the system.

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The alleged manipulation occurred around the market fixes, moments during the day when banks set benchmark prices for currency trades around the world.

The penalty notices for each bank contain specific examples in which traders allegedly manipulated the market to benefit their firms.

In one example, RBS had net client orders to sell British pounds for dollars. This meant the bank would profit if it were able to push the price of pounds lower.

An RBS trader used an online chat room to share information with traders at three other firms, allowing him to increase RBS’s net sell orders to 399 million pounds from 202 million pounds and to push the price on the spot market as low as $1.6213 from $1.6276, regulators found.

The fix was eventually set at $1.6218. As a result, RBS made a profit of $615,000.

In the aftermath, the RBS trader used the chat room to thank his compatriots, saying ‘‘1.6218, nice.’’ One of the other traders replied, ‘‘we ... killed it right,’’ using an obscenity.

Louise Cooper, a former Goldman Sachs stock broker who writes the financial blog CooperCity, said that what was extraordinary about the case is the misconduct occurred when the banks were already under investigation for a similar scandal involving the fixing of the London interbank offered rate, or LIBOR. The industry was well aware that a regulatory backlash was coming.

The US Justice Department is conducting its own criminal investigation of foreign exchange rate setting. And the Federal Reserve confirmed Wednesday that it has an inquiry underway in coordination with Justice and other agencies. More penalties are possible.

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